hamiltonian formulation of systems with linear velocities within riemann liouville fractional derivatives the link between the treatments of constrained systems with fractional derivatives by using both hamiltonian and lagrangian formulations is studied it is shown that both treatments for systems with linear velocities are equivalent

constructing and predicting solitary pattern solutions for nonlinear time fractional dispersive partial differential equations building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics physics and engineering in this work a new analytical technique for constructing and predicting solitary pattern solutions of time fractional dispersive partial differential equations is proposed based on the generalized taylor series formula and residual error function the new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software for method evaluation and validation the proposed technique was applied to three different models and compared with some of the well known methods the resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct as well as the prediction of solitary pattern solutions for time fractional dispersive partial differential equations

numerical solution of fractional partial differential equations with variable coefficients using generalized fractional order legendre functions abstract in this paper a general formulation for the generalized fractional order legendre functions gflfs is constructed to obtain the numerical solution of fractional partial differential equations with variable coefficients the special feature of the proposed approach is that we define generalized fractional order legendre functions over 0 h based on fractional order legendre functions we use these functions to approximate the unknown function on the interval 0 h 0 l in addition the gflfs fractional differential operational and product matrices are driven these matrices combine with tau method to transform the problem to solve systems of linear algebraic equations by solving the linear algebraic equations we can obtain the numerical solution the error analysis shows that the algorithm is convergent the method is tested on examples the results show that the gflfs yields better results

the general vector solutions of such linear coupled matrix fractional differential equations by using kronecker structures in this paper we demonstrate how kronecker products and vector operator can be combined beautifully to solve and fit the non homogenous linear matrix fractional differential equations and such coupled linear matrix fractional differential equations the way exists which transform the given coupled matrix fractional differential equations by using kronecker structures into forms for which solutions may be readily computed some important and interesting special cases of the general system of non homogeneous linear matrix fractional differential equations of fractional order are also considered which includes the non homogenous linear fractional dynamical system with delays in control finally a brief comparison between the fractional and integer order vector solutions and some examples are given to illustrate our new approaches

fractional radiative transfer equation within chebyshev spectral approach in this work we report the convergence of the chebyshev polynomials combined with the s n method for the steady state transport equation using the fractional derivative the procedure is based on the expansion of the angular flux in a truncated series of orthogonal polynomials that results in the transformation of the multidimensional problem into a system of fractional differential equations the convergence of this approach is studied in the context of the multidimensional discrete ordinates equations

classification and unfoldings of degenerate hopf bifurcations abstract this paper initiates the classification up to symmetry covariant contact equivalence of perturbations of local hopf bifurcation problems which do not satisfy the classical non degeneracy conditions the only remaining hypothesis is that i should be simple eigenvalues of the linearized right hand side at criticality then the lyapunov schmidt method allows a reduction to a scalar equation g x 0 where g x g x a definition is given of the codimension of g and a complete classification is obtained for all problems with codimension 3 together with the corresponding universal unfoldings the perturbed bifurcation diagrams are given for the cases with codimension 2 and for one case with codimension 3 for this last case one of the unfolding parameters is a modal parameter such that the topological codimension equals in fact 2 formulas are given for the calculation of the taylor coefficients needed for the application of the results and finally the results are applied to two simple problems a model of glycolytic oscillations and the fitzhugh nerve equations

the adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations in this paper we present the adomian decomposition method and its modifications combined with convergence acceleration techniques such as the diagonal pade approximants and the iterated shanks transforms to solve nonlinear fractional ordinary differential equations two nonlinear numeric examples demonstrate that either the diagonal pade approximants or the iterated shanks transforms can efficiently extend the effective convergence region of the decomposition series solution

chebyshev spectral sn method for the neutron transport equation we study convergence of a combined spectral and sn discrete ordinates approximation for a multidimensional steady state linear transport problem with isotropic scattering the procedure is based on expansion of the angular flux in a truncated series of chebyshev polynomials in spatial variables that results in the transformation of the multidimensional problems into a set of one dimensional problems the convergence of this approach is studied in the context of the discrete ordinates equations based on a special quadrature rule for the scattering integral the discrete ordinates and quadrature errors are expanded in truncated series of chebyshev polynomials of degree l and the convergence is derived assuming l s t 4 p s s where s t and s s are total and scattering cross sections respectively

computations of limit cycles via higher order harmonic balance approximation the detection of limit cycles arising from hopf bifurcation phenomena by applying the harmonic balance method with different higher order approximations is discussed the results are presented using a graphical procedure that indicates clearly how the predictions of amplitude and frequency of a periodic solution can be improved by using higher and higher order approximations complete and explicit formulas for eighth order harmonic balance approximation are provided

an inverse problem of finding a parameter in a semi linear heat equation we consider the following inverse problem of finding the pair u p which satisfies the following u1 uxx p t u f x t u ux p t 0 x 1 0 t t u x 0 u0 x 0 x 1 ux 0 t f t ux 1 t g t 0 t t and 01 x t u x t dx e t 0 t t where u0 f g f and e are known functions the existence uniqueness regularity and the continuous dependence of the solution upon the data are demonstrated

numerical solution of fractional pantograph differential equations by using generalized fractional order bernoulli wavelet in the current study new functions called generalized fractional order bernoulli wavelet functions gfbwfs based on the bernoulli wavelets are defined to obtain the numerical solution of fractional order pantograph differential equations in a large interval for the concept of fractional derivative we will use caputo sense by using riemann liouville fractional integral operator first the generalized fractional order bernoulli wavelets are constructed then these functions and their properties are employed to derive the gfbwfs operational matrices of fractional integration and pantograph the operational matrices of integral and pantograph are utilized to reduce the problem to a set of algebraic equations finally some examples are included for demonstrating the validity and applicability of our method

haar wavelet method for solving fractional partial differential equations numerically in this paper a wavelet operational method based on haar wavelet is proposed to solve the fractional partial differential equations in the caputo derivative sense we give the haar wavelet operational matrix of fractional order integration a truncated haar wavelet series together with the wavelet operational matrix are utilized to reduce the fractional partial differential equations to sylvester equations in addition some examples are presented to show the efficiency and the accuracy of the approach

numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis in this paper a system of nonlinear fractional differential equations fdes are considered they have been solved by legendre wavelets method combining with its operational matrix however there are no articles about solving this system using wavelets method the main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily the convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem finally the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples

block pulse operational matrix method for solving fractional partial differential equation in this paper we first introduce two dimensional block pulse functions and the block pulse operational matrices of the fractional order integration also the block pulse operational matrices of the fractional order differentiation are obtained then we present a computational method based on the above results for solving a class of fractional partial differential equations transforming the initial equation into a sylvester equation the error analysis of the method is given the method is computationally attractive and applications are demonstrated by some numerical examples moreover comparing the methodology with the known technique shows that our approach is more efficient and more convenient

legendre wavelets method for solving fractional partial differential equations with dirichlet boundary conditions in this paper a new method based on the legendre wavelets expansion together with operational matrices of fractional integration and derivative of these basis functions is proposed to solve fractional partial differential equations with dirichlet boundary conditions the proposed method is very convenient for solving such boundary value problems since the boundary conditions are taken into account automatically convergence of the two dimensional legendre wavelets expansion is investigated illustrative examples are included to demonstrate the validity and applicability of the presented wavelets method

nonholonomic constraints with fractional derivatives we consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples the corresponding equations of motion are derived using variational principle we prove that fractional constraints can be used to describe the evolution of dynamical systems in which some coordinates and velocities are related to velocities through a power law memory function

chebyshev polynomials approach for numerically solving system of two dimensional fractional pdes and convergence analysis abstract in this paper an efficient numerical technique based on the chebsyhev orthogonal polynomials is established to obtain the approximate solutions of system of two dimensional fractional order pdes with initial conditions we construct the corresponding differential operational matrix of fractional order and then transform the problem into a system of linear algebra equations compared with other analytical or semi analytical methods ours can achieve better convergence accuracy only small terms are expanded moreover the proposed algorithm is simple in theoretical derivation and numerical simulation in our study the convergence analysis of the system is emphatically investigated than other numerical approaches lastly three numerical examples are applied to test the algorithm and that the obtained numerical results show that our approach is effective and robust

a class of non linear non classical parabolic equations abstract in this paper we deal with a class of non classical parabolic equations which arise from some practical problems such as the identification of unknown parameters free boundary problems etc one of the characteristics of this kind of equation is that the maximum principle is no longer valid we will first study the local solvability for a general equation of this kind via an auxiliary problem and the schauder fixed point principle then some a priori estimates are derived to establish the global existence of the solution moreover uniqueness and continuous dependence of the solution are proved finally some examples are given to illustrate the applications of the theory

numerical solution of one dimensional parabolic inverse problem this paper is concerned with numerical techniques for the solution of a one dimensional parabolic inverse problem with a control parameter the discrete approximation of the problem is based on the finite difference schemes these techniques are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the methods developed here are based on the modified equivalent partial differential equation as described by warming and hyett j comput phys 14 2 1974 159 this approach allows the simple determination of the theoretical order of accuracy thus allowing methods to be compared with one another also from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain free parameters weights thus leading to more accurate methods the results of a numerical experiment are presented and accuracy and the central processor cpu time needed for the parabolic inverse problem are discussed

the hamilton formalism with fractional derivatives recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives in this paper the passage from the lagrangian containing fractional derivatives to the hamiltonian is achieved the hamilton s equations of motion are obtained in a similar manner to the usual mechanics in addition the classical fields with fractional derivatives are investigated using hamiltonian formalism two discrete problems and one continuous are considered to demonstrate the application of the formalism the results are obtained to be in exact agreement with agrawal s formalism

a tau method for the one dimensional parabolic inverse problem subject to temperature overspecification in this work an approximational technique based on shifted legendre tau ideas is presented for the one dimensional parabolic inverse problem with a control parameter the method consists of expanding the required approximate solution as the elements of a shifted legendre polynomial using the operational matrices we reduce the problem to a set of algebraic equations a numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results the method is easy to implement and produces very accurate results

on l factors attached to generic representations of unramified u 2 1 let g be the unramified unitary group in three variables defined over a p adic field with p ne 2 in this paper we establish a theory of newforms for the rankin selberg integral for g introduced by gelbart and piatetski shapiro we describe l and varepsilon factors defined through zeta integrals in terms of newforms we show that zeta integrals of newforms for generic representations attain l factors as a corollary we get an explicit formula for varepsilon factors of generic representations

stability and hopf bifurcation of a general delayed recurrent neural network in this paper stability and bifurcation of a general recurrent neural network with multiple time delays is considered where all the variables of the network can be regarded as bifurcation parameters it is found that hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied by analyzing the characteristic equation and using the frequency domain method the existence of hopf bifurcation is proved the stability of bifurcating periodic solutions is determined by the harmonic balance approach nyquist criterion and graphic hopf bifurcation theorem moreover a critical condition is derived under which the stability is not guaranteed thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood and from which the essential dynamics of the delayed neural network are revealed finally numerical results are given to verify the theoretical analysis and some interesting phenomena are observed and reported

a new approach for solving a system of fractional partial differential equations in this paper we propose a new method for solving systems of linear and nonlinear fractional partial differential equations this method is a combination of the laplace transform method and the iterative method and here after called the iterative laplace transform method this method gives solutions without any discretization and restrictive assumptions the method is free from round off errors and as a result the numerical computations are reduced the fractional derivative is described in the caputo sense finally numerical examples are presented to illustrate the preciseness and effectiveness of the new technique

on shifted jacobi spectral approximations for solving fractional differential equations in this paper a new formula of caputo fractional order derivatives of shifted jacobi polynomials of any degree in terms of shifted jacobi polynomials themselves is proved we discuss a direct solution technique for linear multi order fractional differential equations fdes subject to nonhomogeneous initial conditions using a shifted jacobi tau approximation a quadrature shifted jacobi tau q sjt approximation is introduced for the solution of linear multi order fdes with variable coefficients we also propose a shifted jacobi collocation technique for solving nonlinear multi order fractional initial value problems the advantages of using the proposed techniques are discussed and we compare them with other existing methods we investigate some illustrative examples of fdes including linear and nonlinear terms we demonstrate the high accuracy and the efficiency of the proposed techniques