a generalized treatment of the energetics of translating continua part ii beams and fluid conveying pipes abstract the energetics of translating tensioned beams and fluid transporting pipes under fixed simply supported and free boundary conditions are analyzed in a generalized manner the conservative and non conservative forces acting at the boundaries lead to energy transfer between the translating continua and the boundary supports the forces and associated convective velocities are identified from the one dimensional transport theorem the group velocity and the wavenumber of propagating and evanescent waves in the dispersive continua are defined the time variation of total energy is represented in terms of the impedances and the reflection coefficients of the propagating waves in the continuum and the dynamic stability of the translating continua is discussed based on the energy expressions the critical fluid speed in a cantilevered pipe at which the resultant energy flux into the pipe at the free end vanishes is determined by the use of travelling wave solutions

classical non markovian boltzmann equation the modeling of particle transport involves anomalous diffusion x2 t t with 1 with subdiffusive transport corresponding to 0 1 these anomalies give rise to fractional advection dispersion equations with memory in space and time the usual boltzmann equation with only isolated binary collisions is markovian and in particular the contributions of the three particle distribution function are neglected we show that the inclusion of higher order distribution functions give rise to an exact non markovian boltzmann equation with resulting transport equations for mass momentum and kinetic energy with memory in both time and space the two and the three particle distribution functions are considered under the assumption that the two and the three particle correlation functions are translationally invariant that allows us to obtain advection dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives

new analytical free vibration solutions of orthotropic rectangular thin plates using generalized integral transformation abstract a first endeavor is made to obtain the analytical free vibration solutions of orthotropic rectangular thin plates utilizing the generalized integral transformation technique owing to the nature of the problem it is very hard to get the exact solution of the title problem by common inverse semi inverse method in solution procedure the vibrating beam function is selected as the integral core to form the generalized integral transformation pair then the high order partial differential equation under specific boundary conditions is converted to linear algebraic equations and the exact solution is achieved in a straightforward way one of the advantages of the proposed method is its simplicity and versatility and does not require pre determining the deflection function which makes the solving procedure more reasonable the method has wide applications range and can handle other elastic plate problems such as shear buckling buckling and bending the present results are validated by comparing with the existing analytical solutions which show satisfactory agreement

on the length of simplex paths the assignment case this paper reports on an experimental study of the distribution of the length of simplex paths for the optimal assignment problem we study the distribution of the pivot counts for a version of the simplex method that with essentially equal probabilities introduces any variable with negative reduced cost into the basis in this situation the distribution of the pivot counts turns out to be normally distributed and independent of the actual cost coefficients provided these are sufficiently spread out further the mean and standard deviation grow only moderately with the size of the problem namely asd1 8 andd1 5 respectively for ad d problem implying in particular that the pivot counts concentrate around the mean with growingd the usual simplex method on the other hand gives a growth ofd1 6 hence a large part of the favourable polynomial growth experienced on practical problems may be attributed to the fact that the simplex paths are rather short on the average at least for assignment problems

a new operator splitting method for american options under fractional black scholes models abstract a new operator splitting method is proposed for american options under time fractional black scholes models the fractional linear complementarity problem is split into two easy sub problems with the leading coefficients separated from the convolution sum and matched through a general correction step the method is implementation friendly in the sense that one can easily modify a fractional european solver to obtain the proposed method since the correction step is decoupled and is trivial to solve the method is validated through numerical experiments and demonstrated to be superior to the traditional approach the paper also provides numerical studies including the effect of fractional orders and the comparison of fractional models

combinatorial structure and randomized subexponential algorithms for infinite games the complexity of solving infinite games including parity mean payoff and simple stochastic is an important open problem in verification automata and complexity theory in this paper we develop an abstract setting for studying and solving such games based on function optimization over certain discrete structures we introduce new classes of recursively local global rlg and partial recursively local global prlg functions and show that strategy evaluation functions for simple stochastic mean payoff and parity games belong to these classes in this setting we suggest randomized subexponential algorithms appropriate for rlg and prlg function optimization we show that the subexponential algorithms for combinatorial linear programming due to kalai and matousek sharir welzl can be adapted for optimizing the rlg and prlg functions

a wavelet operational method for solving fractional partial differential equations numerically fractional calculus is an extension of derivatives and integrals to non integer orders and a partial differential equation involving the fractional calculus operators is called the fractional pde they have many applications in science and engineering however not only the analytical solution existed for a limited number of cases but also the numerical methods are very complicated and difficult in this paper we newly establish the simulation method based on the operational matrices of the orthogonal functions we formulate the operational matrix of integration in a unified framework by using the operational matrix of integration we propose a new numerical method for linear fractional partial differential equation solving in the method we 1 use the haar wavelet 2 establish a lyapunov type matrix equation and 3 obtain the algebraic equations suitable for computer programming two examples are given to demonstrate the simplicity clarity and powerfulness of the new method

lie symmetry analysis conservation laws and numerical approximations of time fractional fokker planck equations for special stochastic process in foreign exchange markets abstract in this paper the transition joint probability density function of the solution of the ornstein uhlenbeck process is presented by a deterministic parabolic time fractional pde fpde named time fractional fokker planck equation the article generally is divided to two parts theoretical and approximated analysis in the theoretical sections lie group method and invariant subspace method are applied for finding exact solutions and conservation laws of the considered equation in the next part by chebyshev wavelets s method the numerical solutions are driven then the usefulness of this approximated method is comparing with the exact solutions by some plotted graphs

fractional variational calculus for nondifferentiable functions we prove necessary optimality conditions in the class of continuous functions for variational problems defined with jumarie s modified riemann liouville derivative the fractional basic problem of the calculus of variations with free boundary conditions is considered as well as problems with isoperimetric and holonomic constraints

a fractional calculus of variations for multiple integrals with application to vibrating string we introduce a fractional theory of the calculus of variations for multiple integrals our approach uses the recent notions of riemann liouville fractional derivatives and integrals in the sense of jumarie the main results provide fractional versions of the theorems of green and gauss fractional euler lagrange equations and fractional natural boundary conditions as an application we discuss the fractional equation of motion of a vibrating string

lie symmetry analysis explicit solutions and conservation laws for the space time fractional nonlinear evolution equations abstract this paper studies the symmetry analysis explicit solutions convergence analysis and conservation laws cls for two different space time fractional nonlinear evolution equations with riemann liouville rl derivative the governing equations are reduced to nonlinear ordinary differential equation ode of fractional order using their lie point symmetries in the reduced equations the derivative is in erdelyi kober ek sense power series technique is applied to derive an explicit solutions for the reduced fractional odes the convergence of the obtained power series solutions is also presented moreover the new conservation theorem and the generalization of the noether operators are developed to construct the nonlocal cls for the equations some interesting figures for the obtained explicit solutions are presented

variational problems with fractional derivatives euler lagrange equations we generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized also for the standard case when these two bounds coincide we derive a new form of euler lagrange equations we use approximations for fractional derivatives in the lagrangian and obtain the euler lagrange equations which approximate the initial euler lagrange equations in a weak sense

dynamics of flexible sliding beams non linear analysis part ii transient response in this paper the axially rigid sliding beam problem undergoing small deformations is examined first its governing equation and boundary conditions transformed to the fixed domain and the well known galerkin s approach used to study the transient response of this problem the results obtained are then compared with those in the literature subsequently the authors approach is extended to the non linear axially inextensible sliding beams undergoing large amplitude vibrations and solve several examples to show the differences between the solutions obtained via linear and non linear solvers

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

fractional fokker planck equation solution and application recently metzler et al phys rev lett 82 3563 1999 introduced a fractional fokker planck equation ffpe describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a boltzmann thermal heat bath in this paper we present the solution of the ffpe in terms of an integral transformation the transformation maps the solution of ordinary fokker planck equation onto the solution of the ffpe and is based on levy s generalized central limit theorem the meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk ctrw we investigate in detail i a force free particle ii a particle in a uniform field and iii a particle in a harmonic field we also find an exact solution of the ctrw and compare the ctrw result with the corresponding solution of the ffpe the relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given an example of the one dimensional fractional first passage time in an external linear field is investigated in detail the ffpe is shown to be compatible with the scher montroll approach for dispersive transport and thus is applicable in a large variety of disordered systems the simple ffpe approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena

on a connection between a class of q deformed algebras and the hausdorff derivative in a medium with fractal metric abstract over the recent decades diverse formalisms have emerged that are adopted to approach complex systems amongst those we may quote the q calculus in tsallis version of non extensive statistics with its undeniable success whenever applied to a wide class of different systems kaniadakis approach based on the compatibility between relativity and thermodynamics fractional calculus fc that deals with the dynamics of anomalous transport and other natural phenomena and also some local versions of fc that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations the question we might ask is whether or not there are common aspects that connect these alternative approaches in this short communication we discuss a possible relationship between q deformed algebras in two different contexts of statistical mechanics namely tsallis framework and kaniadakis scenario with local form of fractional derivative operators defined in fractal media the so called hausdorff derivatives mapped into a continuous medium with a fractal measure this connection opens up new perspectives for theories that satisfactorily describe the dynamics for the transport in media with fractal metrics such as porous or granular media possible connections with other alternative definitions of fc are also contemplated insights on complexity connected to concepts like coarse grained space time and physics in general are pointed out

electrified fractional nanofluid flow with suspended carbon nanotubes abstract improvement in thermal and electric conductivity is the basic requirement of many nano electrochemical systems these systems in material science energy management and chemical processing can be efficiently handled with the presence of carbon nanotubes in the base fluid basically nanofluid is used to act as coolant with enhanced thermal conductivity in equipment such as radiators heat exchangers and electronic systems transfer of heat in nanofluids has been discussed by many researchers with ordinary derivative but here we have considered fractional derivatives to achieve more control on heat transfer here in this communication we have discussed two directional viscoelastic fluid flow with suspended carbon nanotubes swcnts as well as mwcnts are considered as nanoparticles in the base fluid in order to achieve control of the flow and heat transfer flow problem is modeled with caputo fractional derivatives along with fractional momentum and thermal relaxation times and 1 in the electrically conducting flow regime electric and magnetic fields are perpendicular to each other and ohmic heating is appropriately handled in energy equation via ohm s law governing fractional pdes are nonlinear in nature and solved numerically with finite difference discretization along with l 1 algorithm simulated results of velocity and temperature are noted for both the swcnts and mwcnts velocity and temperature profiles for mwcnts remained at a higher level when compared to swcnts for all the values of physical parameters the presence of fractional derivatives swcnts and mwcnts made the results valuable that can be used to efficiently handle similar thermal management problems in engineering such as to achieve thermal control in the vehicle engines refrigerators grinders boilers chillers and heat exchangers

different methods for 3 1 dimensional space time fractional modified kdv zakharov kuznetsov equation in this paper the fractional derivatives in the sense of modified riemann liouville derivative and the exp function method the g g expansion method and the generalized kudryashov method are used to construct exact solutions for 3 1 dimensional space time fractional modified kdv zakharov kuznetsov equation this fractional equation can be turned into another nonlinear ordinary differential equation by fractional complex transformation and then these three methods are applied to solve it as a result some new exact solutions are obtained the three methods demonstrate power reliability and efficiency

a closed form approximation for the fractional black scholes model with transaction costs abstract in this paper we investigate option valuation problems under the fractional black scholes model the aim is to propose a pricing formula for the european option with transaction costs where the costs structure contains fixed costs a cost propositional to the volume traded and a cost proportional to the value traded precisely we provide an approximate solution of the nonlinear hoggard whalley wilmott equation the comparison results reveal that our approximate solutions are close to the numerical computations moreover the comparison results demonstrate that the price of the european option decreases as the hurst exponent increases

a numerical method for simulating transverse vibrations of an axially moving string a modified finite difference method is presented to simulate transverse vibrations of an axially moving string by discretizing the governing equation and the stress strain relation at different frictional knots two linear sparse finite difference equations are obtained which can be computed alternatively the numerical method makes the non linear model easier to deal with and of small truncation errors it also shows stable for small initial values so it can be used in analyzing the non linear vibration of viscoelastic moving string efficiently a practical way of testing the precise of the numerical results is given by using a conservative quantity numerical examples are presented and dynamical analysis is given by using the numerical results

a fokker planck equation of fractional order with respect to time by combining the maximum entropy principle with some considerations related to derivatives of fractional order one is led to suggest a fokker planck of fractional order with respect to time which could be related to dynamical systems subject to fractional brownian motion the relation with the process associated with the equation p t 1 n 1 2np x2n is exhibited

recognition problems for special classes of polynomials in 0 1 variables this paper investigates the complexity of various recognition problems for pseudo boolean functions i e real valued functions defined on the unit hypercubebn 0 1 n when such functions are represented as multilinear polynomials in their variables determining whether a pseudo boolean function a is monotonic or b is supermodular or c is threshold or d has a unique local maximum in each face ofbn or e has a unique local maximum inbn is shown to be np hard a polynomial time recognition algorithm is presented for unimodular functions previously introduced by hansen and simeone as a class of functions whose maximization overbn is reducible to a network minimum cut problem

numerical approximation of a time fractional black scholes equation abstract in this paper a time fractional black scholes equation is examined we transform the initial value problem into an equivalent integral differential equation with a weakly singular kernel and use an integral discretization scheme on an adapted mesh for the time discretization a rigorous analysis about the convergence of the time discretization scheme is given by taking account of the possibly singular behavior of the exact solution and first order convergence with respect to the time variable is proved for overcoming the possibly nonphysical oscillation in the computed solution caused by the degeneracy of the black scholes differential operator we employ a central difference scheme on a piecewise uniform mesh for the spatial discretization it is proved that the scheme is stable and second order convergent with respect to the spatial variable numerical experiments support these theoretical results

analytically pricing double barrier options based on a time fractional black scholes equation this paper investigates the pricing of double barrier options when the price change of the underlying is considered as a fractal transmission system in this scenario the option price is governed by a modified black scholes equation with a time fractional derivative in comparison with standard derivatives of integer order the fractional order derivatives are characterized by their globalness i e the rate of change of a function near a point is affected by the property of the function defined in the entire domain of definition rather than just near the point itself the existence of the time fractional derivative in conjunction with the presence of two barriers of the double barrier options has added an additional degree of difficulty not only when a purely numerical solution is sought but also when an analytical method is attempted albeit difficult we have managed to find an explicit closed form analytical solution for double barrier options which has been taken to price the single barrier options and european path independent options under the same framework as a special case of the current solution in addition not only have we provided a theoretical proof for the convergence of the newly found analytic solution in series form which is a vital step to show the closeness of our solution we have also proposed an efficient numerical evaluation technique to facilitate the implementation of our formula so that it can be easily used in trading practice

numerical solution of the time fractional black scholes model governing european options when considering the price change of the underlying fractal transmission system a fractional black scholes b s model with an order time fractional derivative is derived in this paper we discuss the numerical simulation of this time fractional black scholes model tfbsm governing european options a discrete implicit numerical scheme with a spatially second order accuracy and a temporally 2 order accuracy is constructed then the stability and convergence of the proposed numerical scheme are analyzed using fourier analysis some numerical examples are chosen in order to demonstrate the accuracy and effectiveness of the proposed method finally as an application we use the tfbsm and the above numerical technique to price several different european options

on the solutions of nonlinear fractional klein gordon equation with modified riemann liouville derivative abstract in this paper fractional variational iteration method fvim is applied for finding approximate analytical solutions of nonlinear fractional klein gordon equation time fractional derivative is described in the riemann liouville sense a new application of fractional variational iteration method fvim is extended to derive analytical solutions in the form of a series for this equation the behavior of the solutions and the effects of different values of fractional order are indicated graphically it is shown that the solutions obtained by the fvim are reliable convenient and effective for strongly nonlinear partial equations with modified riemann liouville derivative

some distribution independent results about the asymptotic order of the average number of pivot steps of the simplex method this paper is concerned with the average number of pivot steps of the simplex method which are required to solve linear programming problems of the following kind mbox max v t x quad mbox subject to a t i x leq 1 quad mbox for i 1 ldots m mbox where a i v x in mathbb r n we investigate a certain variant of the simplex method which is particularly suited for theoretical considerations for every pair m nm n we introduce probability spaces whose random samples are the linear programming problems of the above mentioned type the vectors ai v are supposed to be distributed independently identically and symmetrically under rotations on a bounded subset of rn we deduce upper and lower bounds for the expectation values of the number of steps required in phase ii of the simplex method the evaluation of these bounds yields the following result for m and for fixed n 1 the expectation values become om1 n 1 2 there exists a distribution whose expectation values increase like m1 n 1 3 for any distribution which satisfies our conditions the expectation values tend to infinity 4 for every e 0 there are distributions whose expectation values become ome

a nonlinear fractional sharma tasso olver equation due to its importance in scientific applications the fractional nonlinear sharma tasso olver equation has been studied by several authors from point of view of exact solutions in this paper new explicit and exact solutions are obtained by using the fractional complex transform and the improved extended tanh coth method the results can be compared with other methods used to solve the same model

stability in parametric resonance of axially moving viscoelastic beams with time dependent speed stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law the kelvin constitution relation and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples are presented for beams with simple supports and fixed supports respectively to demonstrate the effect of viscoelasticity on the stability boundaries in both cases

the simplex algorithm in dimension three we investigate the worst case behavior of the simplex algorithm on linear programs with three variables that is on 3 dimensional simple polytopes among the pivot rules that we consider the random edge rule yields the best asymptotic behavior as well as the most complicated analysis all other rules turn out to be much easier to study but also produce worse results most of them show essentially worst possible behavior this includes both kalai s random facet rule which without dimension restriction is known to be subexponential and zadeh s deterministic history dependent rule for which no nonpolynomial instances in general dimensions have been found so far

modified riemann liouville derivative and fractional taylor series of nondifferentiable functions further results the paper gives some results and improves the derivation of the fractional taylor s series of nondifferentiable functions obtained recently in the form f g h e a h ad g a f g 0 a 1 where e a is the mittag leffier function here one defines fractional derivative as the limit of fractional difference and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using riemann liouville definition as a result a modified riemann liouville definition is proposed which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one s in order to support this f taylor series one shows how its first term can be obtained directly in the form of a mean value formula the fractional derivative of the dirac delta function is obtained together with the fractional taylor s series of multivariate functions the relation with irreversibility of time and symmetry breaking is exhibited and to some extent this f taylor s series generalizes the fractional mean value formula obtained a few years ago by kolwantar

principal parametric resonances of a general continuous system with cubic nonlinearities abstract a generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered the method of multiple scales a perturbation method is used to find an approximate analytical solution the primary parametric resonance of the parametric excitation is considered the amplitude and phase modulation equations are derived steady state solutions and their stability are discussed the solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids natural frequencies of viscoelastic pipes are found frequency response curves and bifurcation points are drawn stable and unstable regions of trivial and nontrivial solutions are obtained

analytical treatment of differential equations with fractional coordinate derivatives this paper outlines a reliable strategy to use the homotopy perturbation method based on jumarie s derivative for solving fractional differential equations in this framework compact structures of fourth order fractional diffusion wave equations are considered as prototype examples moreover convergence of the proposed approach for these types of equations is investigated results show that the response expressions are mittag leffler stable

a review of definitions of fractional derivatives and other operators abstract given the increasing number of proposals and definitions of operators in the scope of fractional calculus it is important to introduce a systematic classification nonetheless many of the definitions that emerged in the literature can not be considered as fractional derivatives we analyze a list of expressions to have a general overview of the concept of fractional integrals derivatives moreover some formulae that do not involve the term fractional are also included due to their particular interest in the area

the first integral method for some time fractional differential equations abstract in this paper the fractional derivatives in the sense of modified riemann liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations the power of this manageable method is presented by applying it to several examples this approach can also be applied to other nonlinear fractional differential equations

on group invariant solutions of fractional order burgers poisson equation abstract in this paper symmetry property of fractional order space time burgers poisson fbp equation is investigated the equation is obtained by replacing first order time and space derivatives to the corresponding fractional derivatives of order and respectively in the classical burgers poisson equation we present lie symmetries and corresponding infinitesimal generators for the fbp equation by using fractional lie group method with the help of these infinitesimal generators some group invariant solutions are sought by reducing the order of the equation

the d step conjecture and its relatives the d step conjecture arose from an attempt to understand the computational complexity of edge following algorithms for linear programming such as the simplex algorithm it can be stated in terms of diameters of graphs of convex polytopes in terms of the existence of nonrevisiting paths in such graphs in terms of an exchange process for simplicial bases of a vector space and in terms of matrix pivot operations first formulated by w m hirsch in 1957 the conjecture remains unsettled though it has been proved in many special cases and counterexamples have been found for slightly stronger conjectures if the conjecture is false as we believe to be the case then finding a counterexample will be merely a small first step in the line of investigation related to the conjecture this report summarizes what is known about the d step conjecture and its relatives a considerable amount of new material is included but it does not seem to come close to settling the conjecture of special interest is the first example of a polytope that is not vertex decomposable showing that a certain natural approach to the conjecture will not work also significant are the quantitative relations among the lengths of paths associated with various forms of the conjecture

generalized einstein relation and the metzler klafter conjecture in a composite subdiffusive regime abstract in this paper a generalized diffusion model driven by the composite subdiffusive fractional brownian motion fbm is employed based on this stochastic process we derive a fractional fokker planck equation ffpe and obtain its solution it is proved that the generalized einstein relation ger and the metzler and klafter conjecture on the asymptotic behavior of stretched gaussian hold the ffpe in a composite subdiffusive regime

affirmative action algorithms affirmative action is a new variety of selection rule which employs historical information to favor the choice of elements that have not been selected in the past we categorize three implementations of this principle and discuss their application to the simplex method to bard type schemes for the linear complementarity problem and to augmenting path methods for network flow problems we present analytical and computational results and some open questions

low order polynomial bounds on the expected performance of local improvement algorithms we present a general abstract model of local improvement applicable to such diverse cases as principal pivoting methods for the linear complementarity problem and hill climbing in artificial intelligence the model accurately predicts the behavior of the algorithms and allows for a variety of probabilistic assumptions that permit degeneracy simulation indicates an approximately linear average number of iterations under a variety of probability assumptions we derive theoretical bounds of 2en logn and en2 for different distributions respectively as well as polynomial bounds for a broad class of probability distributions we conclude with a discussion of the applications of the model to lcp and linear programming

on invariant analysis of some time fractional nonlinear systems of partial differential equations i an investigation of lie point symmetries for systems of time fractional partial differential equations including ito system coupled burgers equations coupled korteweg de vries equations hirota satsuma coupled kdv equations and coupled nonlinear hirota equations has been done using the obtained symmetries each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving erdelyi kober fractional differential operator depending on a parameter

derivation and solutions of some fractional black scholes equations in coarse grained space and time application to merton s optimal portfolio abstract by using the new fractional taylor s series of fractional order f x h e h d x f x where e denotes the mittag leffler function and d x is the so called modified riemann liouville fractional derivative which we introduced recently to remove the effects of the non zero initial value of the function under consideration one can meaningfully consider a modeling of fractional stochastic differential equations as a fractional dynamics driven by a usual gaussian white noise one can then derive two new families of fractional black scholes equations and one shows how one can obtain their solutions merton s optimal portfolio is once more considered and some new results are contributed with respect to the modeling on one hand and to the solution on the other hand finally one makes some proposals to introduce real data and virtual data in the basic equation of stock exchange dynamics

numerical computations of fractional nonlinear hartmann flow with revised heat flux model abstract in this communication we have examined the magneto hydrodynamic flow of viscoelastic liquid with revise version of thermal flux thermal conductivity of the fluid is variable effects of body forces such as gravity are also examined in terms of convection non integer time derivatives are used for the better understanding of viscoelastic flow characteristics in literature these derivatives have been proved suitable for the predictions of hereditary systems such as viscoelastic flows heat transfer is analyzed in the flow field via modified fractional thermal gradient temperature gradient exists between the flow boundaries and increases with the passage of time flow is generated by the variable movement of flow boundary all the segments of numerical modeling are completely addressed in this paper i e physical system mathematical model simulation prediction validation and verification unsteady motion of in compressible fluid is directed by differential equations with fractional partial derivatives for the solutions of these equations numerical techniques are necessary to use governing equations with appropriate flow conditions have been discretized by finite difference along with finite element algorithms theoretical error appraisals are hypothesized and created numerical plan has been approved by doing error investigations numerically regarding spatial directions we have shown the estimate error and plotted the error curves in logarithmic scales of l 2 and h 1 norms by taking absolute approximations of the space discretization local nusselt number and coefficients of skin friction are determined for non integer viscoelastic model flow field is simulated for various values of physical parameters the obtained results showed that fractional exponent has opposite effects on the velocity temperature profiles for time t 2 it is also noted that temperature gradient increases by the increase of fractional number and thermal relaxation parameter viscoelastic flows in polymer and plastics industries can be addressed by similar technique

the fractional quadratic form identity and hamiltonian structure of an integrable coupling of the fractional ablowitz kaup newell segur hierarchy starting from a general isospectral problem of fractional order we propose a fractional quadratic form identity from which the hamiltonian structure of an integrable coupling of the fractional ablowitz kaup newell segur hierarchy is derived the method can be generalized to other fractional integrable couplings

derivation of a new mertons optimal problem presented by fractional stochastic stock price and its applications in this article a new model of mertons optimal problem is derived this derivation is based on stock price presented by fractional order stochastic differential equation an extension of hamiltonjacobibellman is used to transfer our proposed model to a fractional partial differential equation as an application of our proposed model two optimal problems are discussed and solved analytically

a generalized fractional trace identity and hamiltonian structure of the fractional soliton equation hierarchy a generalized fractional trace identity and hamiltonian structure of the fractional soliton equation hierarchy are presented by using the modified riemann liouville derivative and exterior derivatives of fractional orders example of the fractional kaup newell kn soliton equation hierarchy and hamiltonian system are considered which is a new integrable hierarchy and possesses hamiltonian structure

fast numerical simulation of a new time space fractional option pricing model governing european call option abstract when the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a levy distribution a time space fractional option pricing model tsfopm is obtained then we discuss the numerical simulation of the tsfopm a discrete implicit numerical scheme with a second order accuracy in space and a 2 order accuracy in time is constructed where is a transmission exponent the stability and convergence of the obtained numerical scheme are analyzed moreover a fast bi conjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method finally the tsfopm and the above numerical technique are applied to price european call option the characteristics of the fractional option pricing model are analyzed in comparison with the classical black scholes b s model

application of the differential transformation method to vibration analysis of pipes conveying fluid abstract in this paper a relatively new semi analytical method called differential transformation method dtm is generalized to analyze the free vibration problem of pipes conveying fluid with several typical boundary conditions the natural frequencies and critical flow velocities are obtained using dtm the results are compared with those predicted by the differential quadrature method dqm and with other results reported in the literature it is demonstrated that the dtm has high precision and computational efficiency in the vibration analysis of pipes conveying fluid

the efficiency of the simplex method a survey the linear programming problem is by far the most widely used optimization model its impact on economic and government modeling is immense the simplex method for solving the linear programming lp problem due to george dantzig has been an extremely efficient computational tool for almost four decades the method has been the subject of intense investigations for many years but some major aspects of its behavior are not fully understood yet the purpose of this paper is to survey the body of knowledge on the efficiency of the simplex method from both practical and theoretical points of view adopting the number of iterations pivot steps as the yardstick for efficiency we survey four aspects of the issue 1 reports on practical experience of the method s performance on real life lp problems 2 results on controlled monte carlo experiments solving lp problems which were randomly generated according to some predetermined distributions 3 complexity results including theoretical analyses on both upper and lower bounds for the performance of the simplex as well as non simplex algorithms for lp 4 results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the simplex method we discuss the consequences and limitations of the various studies special emphasis is given to open questions

stochastic calculus for fractional brownian motion i theory in this paper a stochastic calculus is given for the fractional brownian motions that have the hurst parameter in 1 2 1 a stochastic integral of ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment this integral uses the wick product and a derivative in the path space some ito formulae or change of variables formulae are given for smooth functions of a fractional brownian motion or some processes related to a fractional brownian motion a stochastic integral of stratonovich type is defined and the two types of stochastic integrals are explicitly related a square integrable functional of a fractional brownian motion is expressed as an infinite series of orthogonal multiple integrals

a simple heuristic approach to simplex efficiency abstract consider the standard linear program minimize cx subject to ax b x 0 where a is an m n matrix the simplex algorithm solves this linear program by moving from an extreme point of the feasibility region to a better in terms of the objective function cx extreme point via the pivot operation until the optimal is reached in order to obtain a feel for the number of necessary iterations we consider a simple probabilistic markov chain model as to how the algorithm moves along the extreme points at first we suppose that if at any time the algorithm is at the j th best extreme point then after the next pivot the resulting extreme point is equally likely to be any of the j 1 best under this assumption we show that the time to get from the n th best to the best extreme point has approximately for large n a poisson distribution with mean equal to the algorithm base e of n we also consider a more general probabilistic model in which we drop the uniformity assumption and suppose that when at the j th best the next one is chosen probabilistically according to weights w i i 1 j 1

dynamic analysis of axially moving orthotropic plates integral transform solution the generalized integral transform technique gitt is employed to obtain a hybrid analytical numerical solution for dynamic response of axially moving orthotropic plates considering two combinations of simply supported s and clamped c boundary conditions ccss and cccc through the double integral transform for the transverse displacement field in the x and y directions the implementation of gitt approach for analyzing the forced vibration equation eliminates the space variable and leads to a coupled system of second order ordinary differential equations odes in the dimensionless temporal variable the mathematica s built in function ndsolve is employed to numerically solve the resulting transformed ode system excellent convergence behavior of the proposed eigenfunction expansions is demonstrated for calculating the transverse displacement at various points of axially moving orthotropic plates the first sixteen mode shapes of vibration for axially moving plates are graphically illustrated the proposed approach is verified by comparing the transverse vibration displacement of central point displacement profiles along the symmetric lines and natural circular frequencies of the plate for zero moving velocity case with the corresponding results obtained by abaqus finite element program moreover parametric studies are performed to analyze the effects of flexural rigidity ratio dimensionless axial speed and aspect ratio on the vibration amplitude of moving plates

a conserved quantity and the stability of axially moving nonlinear beams free nonlinear transverse vibration is investigated for an axially moving beam modeled by an integro partial differential equation based on the equation a conserved quantity is defined and confirmed for axially moving beams with pinned or clamped ends the conserved quantity is applied to demonstrate the lyapunov stability of the straight equilibrium configuration in transverse nonlinear of beam with a low axial speed

estimation of unknown function of a class of integral inequalities and applications in fractional integral equations in this paper we establish a class of iterated integral inequalities which includes a nonconstant term outside the integrals the upper bound of the embedded unknown function is estimated explicitly by adopting novel analysis techniques such as change of variable amplification method differential and integration the derived result can be applied in the study of qualitative properties of solutions of fractional integral equations

option pricing beyond black scholes based on double fractional diffusion abstract we show how the prices of options can be determined with the help of double fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the black scholes formula

on the average length of lexicographic paths a bound is given for the average length of a lexicographic path a definition that is motivated by degeneracies encountered when using the randomized simplex method

bifurcation and exact traveling wave solutions for dual power zakharov kuznetsov burgers equation with fractional temporal evolution abstract in this article we introduce the dual power zakharov kuznetsov burgers equation with fractional temporal evolution in the sense of modified riemann liouville derivative we investigate the dynamical behavior bifurcations and phase portrait analysis of the exact traveling wave solutions of the system with and without damping effect we apply the g g expansion method in context of fractional complex transformation and seek a variety of exact traveling wave solutions including solitary wave kink type wave breaking wave and periodic wave solutions of the equation furthermore the remarkable features of the traveling wave solutions and phase portraits of dynamical system are demonstrated through interesting figures

the hirsch conjecture for dual transportation polyhedra an algorithm is given that joins any pair of extreme points of a dual transportation polyhedron by a path of at most m 1 n 1 extreme edges

group analysis and exact solutions of the time fractional fokker planck equation abstract in this paper the lie symmetry analysis method is extended to deal with the nonlinear time fractional fokker planck fp equation with riemann liouville derivative the erdelyi kober fractional derivative which is depending on a parameter is used for the reduction of fp equation symmetry reduction is provided and some exact analytic solutions to the time fractional fp equation are investigated by virtue of the reduction method introduced by m c nucci

dynamic response of clamped axially moving beams integral transform solution the generalized integral transform technique gitt is employed to obtain a hybrid analytical numerical solution for dynamic response of clamped axially moving beams the use of the gitt approach in the analysis of the transverse vibration equation leads to a coupled system of second order differential equations in the dimensionless temporal variable the resulting transformed ode system is then solved numerically with automatic global accuracy control by using the subroutine divpag from imsl library excellent convergence behavior is shown by comparing the vibration displacement of different points along the beam length numerical results are presented for different values of axial translation velocity and flexural stiffness a set of reference results for the transverse vibration displacement of axially moving beam is provided for future co validation purposes

local fractional fokker planck equation we propose a new class of differential equations which we call local fractional differential equations they involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time a local fractional analog of the fokker planck equation has been derived starting from the chapman kolmogorov condition we solve the equation with a specific choice of the transition probability and show how subdiffusive behavior can arise

thermal wave model of bioheat transfer with modified riemann liouville fractional derivative in this paper a new fractional thermal wave model of the bioheat transfer ftwmbt caused by spatial heating is built using taylor s series expansion of modified riemann liouville fractional derivatives a one dimensional analytical solution of the ftwmbt in a finite medium is obtained the ftwmbt in the case 1 interpolates the standard thermal wave model of bioheat transfer and the well known pennes bioheat equation 0 finally numerical results are presented graphically for various values of different parameters this study demonstrates that fractional models can provide a unified approach to examine the heat transfer in biological tissue

solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach adomian meyers modified decomposition method abstract in this paper we present the generalized adomian rach theorem and the generalized rach adomian meyers modified decomposition method for solving multi order nonlinear fractional ordinary differential equations we consider different classes of initial value problems for nonlinear fractional ordinary differential equations including the case of real valued orders and another case of rational valued orders which are solved by the present method this method can treat any analytic nonlinearity the coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme which does not involve integration operations compared with the classic adomian decomposition method

on the fractional solution of the equation f x y f x f y and its application to fractional laplace s transform abstract it is shown that if the problem is defined in the setting of fractional calculus via fractional difference on non differentiable functions then the solution of the functional equation f x y f x f y is exactly defined as the solution of a linear fractional differential equation the dual or counterpart problem that is the fractional solution of the equation g xy g x g y is also considered and it is shown that the corresponding solution is the logarithm of fractional order defined as the inverse of a generalized mittag leffler function which is nowhere differentiable this framework suggests a definition of fractional laplace s transform expressed in terms of generalized mittag leffler function and its main properties are outlined mainly inverse function and convolution one takes this opportunity to display a new fractional taylor s series for functions f x y of two variables x and y many open problems are stated which are directly related to the non differentiability of the functions so involved therefore the title on the fractional solution

bmo and morrey campanato estimates for stochastic convolutions and schauder estimates for stochastic parabolic equations abstract in this paper we are aiming to prove several regularity results for the following stochastic fractional heat equations with additive noises d u t x 2 u t x d t g t x d t u 0 0 t 0 t x g for a random field u t x 0 t g u t x u t x r where 2 2 0 2 is the fractional laplacian t 0 is arbitrarily fixed g r d is a bounded domain g 0 t g r is a joint measurable coefficient and t t 0 is either a brownian motion or a levy process on a given filtered probability space f p f t t 0 t to this end we derive the bmo estimates and morrey campanato estimates respectively for stochastic singular integral operators arising from the equations concerned then by utilizing the embedding theory between the campanato space and the holder space we establish the controllability of the norm of the space c 2 d where 0 d 0 t g with all these in hand we are able to show that the q th order bmo quasi norm of the q 0 order derivative of the solution u is controlled by the norm of g under the condition that t is a levy process finally we derive the schauder estimate for the p moments of the solution of the above stochastic fractional heat equations driven by levy noise

analysis of lie symmetries with conservation laws and solutions for the generalized 3 1 dimensional time fractional camassa holm kadomtsev petviashvili equation abstract in this paper under investigated is a generalized 3 1 dimensional camassa holm kadomtsev petviashvili gch kp equation which describes the role of dispersion in the formation of patterns in liquid drops with the help of the semi inverse method the euler lagrange equation and agrawal s method the time fractional gch kp equation is derived in the sense of riemann liouville fractional derivatives further the symmetry of the 3 1 dimensional time fractional gch kp equation is studied by fractional order symmetry meanwhile based on the new conservation theorem the conservation laws of 3 1 dimensional time fractional gch kp equation are constructed finally the solutions to the equation are given via a bilinear method and the radial basis functions rbfs meshless approach

analytical approximate solutions for nonlinear fractional differential equations we consider a class of nonlinear fractional differential equations fdes based on the caputo fractional derivative and by extending the application of the adomian decomposition method we derive an analytical solution in the form of a series with easily computable terms for linear equations the method gives exact solution and for non linear equations it provides an approximate solution with good accuracy several examples are discussed

computing the dynamic response of an axially moving continuum the aim of this study was to apply an approximate galerkin finite element method to solve the initial boundary value problem of a viscously damped axially moving pre tensioned beam including arbitrary support excitations in order to validate the galerkin finite element method the results were compared with exact solutions when available and with solutions obtained using the finite difference and galerkin methods the energy dissipation of the system was considered in the form of an equivalent viscous damping model it was also shown that for certain values of the parameters especially at high velocities the galerkin method using stationary string eigenfunctions can give a poor prediction of the dynamic response

derivation of an amplitude of information in the setting of a new family of fractional entropies by generalizing the basic functional equation f xy f x f y in the form f b xy f b x f b y b 1 one can derive a family of solutions which are exactly the inverse of the mittag leffler function referred to as mittag leffler logarithm or logarithm of fractional order this result provides a new family of generalized informational entropies which are indexed by a parameter clearly related to fractals via fractional calculus and which is quite relevant in the presence in defect of observation the relation with shannon s entropy renyi s entropy and tsallis entropy is clarified and it is shown that tsallis generalized logarithm has a significance in terms of fractional calculus the case b 2 looks like directly relevant to amplitude of probability in quantum mechanics and provides an approach to the definition of amplitude of informational entropy one examines the kind of result one can so obtain in applying the maximum entropy principle in the presence of uncertain definition or fuzzy definition the mittag leffler function would be more relevant than the gaussian normal law to some extent this new formulation could be fully supported by the derivation of a new family of fractional fisher information

a fractional variational iteration method for solving fractional nonlinear differential equations recently fractional differential equations have been investigated by employing the famous variational iteration method however all the previous works avoid the fractional order term and only handle it as a restricted variation a fractional variational iteration method was first proposed in g c wu e w m lee fractional variational iteration method and its application phys lett a 374 2010 2506 2509 and gave a generalized lagrange multiplier in this paper two fractional differential equations are approximately solved with the fractional variational iteration method

idea of invariant subspace combined with elementary integral method for investigating exact solutions of time fractional npdes abstract in this paper inspired by the idea of invariant subspace method and combined with elementary integral method we introduced a novel approach for investigating exact solutions of a time fractional nonlinear partial differential equation npde based on hypothetical structure of solution of separated variable a time fractional npde defined by time and space variables can be reduced to a nonlinear ordinary differential equation node or nodes defined by space variable alone and then using the elementary integral method to solve the node or nodes different kinds of exact solutions of a time fractional npde are obtained finally as examples the time fractional hunter saxton equation and time fractional li olver equation were studied different kinds of exact solutions of these equations were obtained and their dynamical properties were illustrated

new solitary wave solutions of 2 1 dimensional space time fractional burgers equation and korteweg de vries equation abstract in this article via the improved fractional subequation method the fully analytical solutions of the 2 1 dimensional space time fractional burgers equation and korteweg de vries equation involving jumarie s modified riemann liouville derivative have been derived as a result with the aid of symbolic computation many types of new analytical solutions are obtained which include new solitary wave periodic wave and rational wave solutions the graphical representations show that these gained solutions have abundant structures

simulations of transverse vibrations of an axially moving string a modified difference approach a modified finite difference approach to simulate transverse vibrations of an axially moving string is presented the stress is treated as a new unknown in discretization of the spatial variable a set of differential algebraic equations is established based on the discreted governing equation and the constitutive relation for linear vibrations a conserved functional is employed to test the algorithm and the 1 2 3 4 term truncated modal analytical solutions are compared with the numerical solution for the free nonlinear vibration a new conserved functional is used to check the algorithm effects of the transport speed on the free and forced nonlinear vibrations are numerically investigated

lie symmetry analysis of the time fractional kdv type equation abstract the lie symmetry analysis method is extended to deal with the time fractional kdv type equation it is shown that this equation can be reduced to an equation with the erdelyi kober fractional derivative this method can also be applied to symmetry classification of fractional equations with some arbitrary functions

holder continuous of the solutions to stochastic nonlocal heat equations abstract in this paper we aim to obtain the holder continuous of solutions to stochastic nonlocal heat equations by using campanato estimates and sobolev embedding theorem we first prove the holder continuous of the mild solution of stochastic nonlocal diffusion equations locally in r d in the sense that the solution u belongs to the space c d t l p then by using tail estimates we obtain the estimates of the mild solution in l p c d t lastly we prove the holder continuous of the mild solution on bounded domain

the application of fractional derivatives in stochastic models driven by fractional brownian motion abstract in this paper in order to establish connection between fractional derivative and fractional brownian motion fbm we first prove the validity of the fractional taylor formula proposed by guy jumarie then by using the properties of this taylor formula we derive a fractional ito formula for h 1 2 1 which coincides in form with the one proposed by duncan for some special cases whose formula is based on the wick product lastly we apply this fractional ito formula to the option pricing problem when the underlying of the option contract is supposed to be driven by a geometric fractional brownian motion the case that the drift volatility and risk free interest rate are all dependent on t is also discussed

new approach to find exact solutions of time fractional kuramoto sivashinsky equation abstract in the present paper we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics viz time fractional kuramoto sivashinsky equation by a new proposed method via fractional complex transform as a result new types of exact analytical solutions are obtained here the fractional derivative is described in jumarie s modified riemann liouville sense