a unified method for the design of nonovershooting linear multivariable state feedback tracking controllers we consider the use of linear multivariable feedback control to achieve a nonovershooting step response a method is given for designing a linear time invariant state feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time under some mild assumptions we present a unified design method that can be applied to continuous and discrete time systems square and non square systems minimum and nonminimum phase systems and also strictly proper and nonstrictly proper systems

on generalized fractional integral inequalities for twice differentiable convex functions abstract in this article some new generalized fractional integral inequalities of midpoint and trapezoid type for twice differentiable convex functions are obtained in view of this we obtain new integral inequalities of midpoint and trapezoid type for twice differentiable convex functions in a form classical integral and riemann liouville fractional integrals finally we apply our new inequalities to construct inequalities involving moments of a continuous random variable

application of subival in solving initial value problems with fractional derivatives abstract the application of a numerical method for the approximation of the fractional derivative in riemann liouville and caputo definitions in initial value problems is discussed the method previously known as the subinterval based method is now referred to by its acronym subival for simpler future references it is dependent on subinterval partitions performed according to a proposed algorithm interpolations using selected time axis nodes i e nodes where solutions have been computed and analytical monomial integrodifferentiation formulae two exemplary circuit problems have been introduced as a test for the method these problems have analytical solutions available in literature the evaluations of these solutions have been compared with results obtained through an adaptive step size predictor corrector scheme where the core computations relied on the proposed numerical method subival has been implemented into an activex dynamic link library dll the paper contains instructions on how the predictor corrector algorithm can be implemented into a computer algebra system where the subival library is applied for the fractional derivative approximation examples of this are given in the form of scripts in matlab and mathematica these scripts generally allow to solve systems of fractional order state equations to which the introduced circuit examples can be brought to

zeta function regularization the multiplicative anomaly and the wodzicki residue the multiplicative anomaly associated with the zeta function regularized determinant is computed for the laplace type operators v1 v1 and v2 v2 with v1 v2 constant in a d dimensional compact smooth manifold md making use of several results due to wodzicki and by direct calculations in some explicit examples it is found that the multiplicative anomaly is vanishing for d odd and for d 2 an application to the one loop effective potential of the o 2 self interacting scalar model is outlined

heat kernel coefficients of the laplace operator on the d dimensional ball we present a very quick and powerful method for the calculation of heat kernel coefficients it makes use of rather common ideas as integral representations of the spectral sum mellin transforms non trivial commutation of series and integrals and skillful analytic continuation of zeta functions on the complex plane we apply our method to the case of the heat kernel expansion of the laplace operator on a d dimensional ball with either dirichlet neumann or in general robin boundary conditions the final formulas are quite simple using this case as an example we illustrate in detail our scheme which serves for the calculation of an in principle arbitrary number of heat kernel coefficients in any situation when the basis functions are known we provide a complete list of new results for the coefficients b3 b10 corresponding to the d dimensional ball with all the mentioned boundary conditions and d 3 4 5

conditions that guarantee no overshoot for linear systems in practical control problems it is often desirable to make setpoint changes without overshoot in this paper necessary and sufficient conditions are presented which guarantee that linear state space models will not exhibit overshoot several examples illustrate the utility and simplicity of the new results

generalized conformable fractional operators abstract in 2015 abdeljawad 1 has put an open problem which is stated as is it hard to fractionalize the conformable fractional calculus either by iterating the conformable fractional derivative grunwald letnikov approach or by iterating the conformable fractional integral of order 0 1 riemann approach notice that when 0 we obtain hadamard type fractional integrals in this article we claim that yes it is possible to iterate the conformable fractional integral of order 0 1 riemann approach such that when 0 we obtain hadamard fractional integrals first of all we prove cauchy integral formula for repeated conformable fractional integral and proceed to define new generalized conformable fractional integral and derivative operators left and right sided we also prove some basic properties which are satisfied by these operators these operators integral and derivative are the generalizations of katugampola operators riemann liouville fractional operators hadamard fractional operators we apply our results to a simple function also we consider a nonlinear fractional differential equation using this new formulation we show that this equation is equivalent to a volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear problem at the end we give conclusion and point out an open problem

global convergence of successive approximations for partial hadamard integral equations and inclusions abstract this paper deals with the global convergence of successive approximations as well as the uniqueness of solutions for some classes of partial functional hadamard integral equations and inclusions we prove a theorem on the global convergence of successive approximations to the unique solution of our problems

toward a theory of rank one attractors introduction 1 statement of results part i preparation 2 relevant results from one dimension 3 tools for analyzing rank one maps part ii phase space dynamics 4 critical structure and orbits 5 properties of orbits controlled by critical set 6 identification of hyperbolic behavior formal inductive procedure 7 global geometry via monotone branches 8 completion of induction 9 construction of srb measures part iii parameter issues 10 dependence of dynamical structures on parameter 11 dynamics of curves of critical points 12 derivative growth via statistics 13 positive measure sets of good parameters appendices

synchronization of nonlinear fractional order systems by means of pirα reduced order observer this paper deals with the master slave synchronization scheme for partially known nonlinear fractional order systems where the unknown dynamics are considered as the master system and we propose the slave system structure which estimates the unknown state variables besides it is introduced a new fractional model free reduced order observer inspired on the new concept of fractional algebraic observability fao we applied the results to a rossler hyperchaotic fractional order system and lorenz fractional order system and by means of some simulations we show the effectiveness of the suggested approach

computing hadamard type operators of variable fractional order abstract we consider hadamard fractional derivatives and integrals of variable fractional order a new type of fractional operator which we call the hadamard marchaud fractional derivative is also considered the objective is to represent these operators as series of terms involving integer order derivatives only and then approximate the fractional operators by a finite sum an upper bound formula for the error is provided we exemplify our method by applying the proposed numerical procedure to the solution of a fractional differential equation and a fractional variational problem with dependence on the hadamard marchaud fractional derivative

fuzzy fractional differential equations under caputo katugampola fractional derivative approach abstract in this work an initial value problem of caputo katugampola ck fractional differential equations in fuzzy setting is considered and an idea of successive approximations under generalized lipschitz condition is used to prove the existence and uniqueness results of the solution to the given problem in order to obtain the above results some necessary comparison theorems in real valued differential equation under ck fractional derivative are established finally a new technique to find analytical solutions of ck fuzzy fractional differential equations by using the solutions of fuzzy integer order differential equations is proposed some examples illustrating the applications of our results are presented

non local fractional calculus from different viewpoint generated by truncated m derivative abstract the core of this paper is to propose more favored novel non local fractional integral and derivative operators with three parameters by using the iteration manner on truncated m derivative involving truncated mittag leffler function this is related closely to the fact that in a certain sense to iterate a convenient local derivative for real phenomena under investigation is one of the best ways for obtaining more comprehensive fractional integration and differentiation in order to gain a deeper grip we address some significant theorems reflected accomplishedly the features of the standard fractional calculus about these aidful operators encompassing some other types of fractional operators the presented new operators in riemann liouville and caputo sense are utilized to solve sturm liouville problem subjected to the initial conditions as a useful method laplace transform of the aforementioned fractional integral and derivative is introduced to solve anomalous dynamics of various complex systems moreover we carry out comparison analysis by plotting governing sturm liouville equation in order to grasp the advantages of these new fractional operators performing much better on account of the additional parameter

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

on the range and invertibility of a class of mellin multiplier transforms i abstract we study the range and invertibility in weighted versions of lp 0 of the operators nm and ml whose mellin multipliers are s m and s l respectively we deduce corresponding results for the laplace transform which generalise those of widder the paper is the first of a series concerning operators whose multipliers involve products and quotients of gamma functions and which include as special cases operators with g function kernels studied by rooney

applications of fractional calculus in solving abel type integral equations surface volume reaction problem abstract in this paper we consider a class of partial integro differential equations of fractional order motivated by an equation which arises as a result of modeling surface volume reactions in optical biosensors we solve these equations by employing techniques from fractional calculus several examples are discussed furthermore for the first time we encounter an order of the fractional derivative other than 1 2 in an applied problem hence in this paper we explore the applicability of fractional calculus in real world applications further strengthening the true nature of fractional calculus

properties of the katugampola fractional derivative with potential application in quantum mechanics katugampola e print arxiv 1410 6535 recently introduced a limit based fractional derivative d referred to in this work as the katugampola fractional derivative that maintains many of the familiar properties of standard derivatives such as the product quotient and chain rules typically fractional derivatives are handled using an integral representation and as such are non local in character the current work starts with a key property of the katugampola fractional derivative d y t1 dydt and the associated differential operator d t1 d1 these operators their inverses commutators anti commutators and several important differential equations are studied the anti commutator serves as a basis for the development of a self adjoint operator which could potentially be useful in quantum mechanics a hamiltonian is constructed from this operator and applied to the particle in a box model

one loop stress tensor renormalization in curved background the relation between ζ function and point splitting approaches and an improved point splitting procedure we conclude the rigorous analysis of a previous paper v moretti commun math phys 201 327 1999 concerning the relation between the euclidean point splitting approach and the local function procedure to renormalize physical quantities at one loop in euclidean quantum field theory in curved space time the case of the stress tensor is now considered in general d dimensional closed manifolds for positive scalar operators v x results obtained formally in previous works in the case d 4 and v x r x m2 are rigorously proven and generalized it is also proven that in static euclidean manifolds the method is compatible with lorentzian time analytic continuations it is proven that the result of the function procedure is the same obtained from an improved version of the point splitting method which uses a particular choice of the term w0 x y in the hadamard expansion of the green s function given in terms of heat kernel coefficients this version of the point splitting procedure works

mellin transforms of generalized fractional integrals and derivatives we obtain the mellin transforms of the generalized fractional integrals and derivatives that generalize the riemann liouville and the hadamard fractional integrals and derivatives we also obtain interesting results which combine generalized r m operators with generalized stirling numbers and lah numbers for example we show that 1 1 corresponds to the stirling numbers of the 2nd kind and 2 1 corresponds to the unsigned lah numbers further we show that the two operators r m and m r r m n generate the same sequence given by the recurrence relation s n k i 0 r m m r n 2 k i 1 r i r i s n 1 k i 0 k n with s 0 0 1 and s n 0 s n k 0 for n 0 and 1 min r m n 1 k or k 0 finally we define a new class of sequences for r 1 3 1 4 1 5 1 6 and in turn show that 1 2 1 corresponds to the generalized laguerre polynomials

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

comments on the stress energy tensor operator in curved spacetime the technique based on a algebra of wick products of field operators in curved spacetime in the local covariant version proposed by hollands and wald is strightforwardly generalized in order to define the stress energy tensor operator in curved globally hyperbolic spacetimes in particular the locality and covariance requirement is generalized to wick products of differentiated quantum fields within the proposed formalism there is room to accomplish all of the physical requirements provided that known problems concerning the conservation of the stress energy tensor are assumed to be related to the interface between the quantum and classical formalism the proposed stress energy tensor operator turns out to be conserved and reduces to the classical form if field operators are replaced by classical fields satisfying the equation of motion the definition is based on the existence of convenient counterterms given by certain local wick products of differentiated fields these terms are independent from the arbitrary length scale and any quantum state and they classically vanish on solutions of the klein gordon equation considering the averaged stress energy tensor with respect to hadamard quantum states the presented definition turns out to be equivalent to an improved point splitting renormalization procedure which makes use of the nonambiguous part of the hadamard parametrix only that is determined by the local geometry and the parameters which appear in the klein gordon operator in particular no extra added by hand term g q and no arbitrary smooth part of the hadamard parametrix generated by some arbitrary smooth term 0 are involved the averaged stress energy tensor obtained by the point splitting procedure also coincides with that found by employing the local function approach whenever that technique can be implemented

non stationary non uniform hyperbolicity srb measures for dissipative maps we prove the existence of srb measures for diffeomorphisms where a positive volume set of initial conditions satisfy an effective hyperbolicity condition that guarantees certain recurrence conditions on the iterates of lebesgue measure we give examples of systems that do not admit a dominated splitting but can be shown to have srb measures using our methods

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

nonovershooting and monotone nondecreasing step responses of a third order siso linear system this paper presents the necessary and sufficient conditions for a third order single input single output siso linear system to have a nonovershooting or monotone nondecreasing step response if the transfer function of an overall system has real poles a necessary and sufficient condition is found for the nonovershooting or monotone nondecreasing step response in the case of complex poles one sufficient condition and two necessary conditions are obtained the resulting conditions are all in terms of the coefficients of the numerator of the transfer function simple calculations can be used to check a system for the nonovershooting or monotone nondecreasing step response another feature is that the conditions in terms of pole zero configurations can be easily derived from the present results

mellin transforms and asymptotics harmonic sums this survey presents a unified and essentially self contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics discrete probabilistic models and the average case analysis of algorithms it relies on the mellin transform a close relative of the integral transforms of laplace and fourier the method applies to harmonic sums that are superpositions of rather arbitrary harmonics of a common base function its principle is a precise correspondence between individual terms in the asymptotic expansion of an original function and singularities of the transformed function the main applications are in the area of digital data structures probabilistic algorithms and communication theory

srb measures for attractors with continuous invariant splittings we study the existence of srb measures of c 2 diffeomorphisms for attractors whose bundles admit holder continuous invariant non dominated splittings we prove the existence when one sub bundle has the non uniform expanding property on a set with positive lebesgue measure and the other sub bundle admits non positive lyapunov exponents on a total probability set

regional observability for hadamard caputo time fractional distributed parameter systems abstract in this paper regional gradient exact and approximate observability problems are studied on hadamard caputo time fractional distributed parameter systems without any knowledge of the initial vector and its gradient several equivalent criteria are first provided to achieve the regional observability based on these characterizations for both strategic and gradient strategic zone sensors are developed then by employing the hilbert uniqueness method hum we explicitly reconstruct the initial vector and its gradient respectively a one dimension example is finally included to illustrate our results

compositions of hadamard type fractional integration operators and the semigroup property abstract this paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of hadamard in the space xcp of functions f on r 0 such that 0 u c f u p du u ess sup u 0 u c f u for c r in particular in the space lp 0 1 p the semigroup property and its generalizations are established for the generalized hadamard type fractional integration operators under consideration conditions are also given for the boundedness in xcp of these operators they involve kummer confluent hypergeometric functions as kernels

zeta functions formulas and applications abstract the existence conditions of the zeta function of a pseudodifferential operator and the definition of determinant thereby obtained are reviewed as well as the concept of multiplicative anomaly associated with the determinant and its calculation by means of the wodzicki residue exponentially fast convergent formulas valid in the whole of the complex plane and yielding the pole positions and residua that extend the ones by chowla and selberg for the epstein zeta function quadratic form and by barnes affine form are then given after briefly recalling the zeta function regularization procedure in quantum field theory some applications of these expressions in physics are described

hermite hadamard and hermite hadamard fejer type inequalities for generalized fractional integrals abstract in this paper we obtain the hermite hadamard and hermite hadamard fejer type inequalities for fractional integrals which generalize the two familiar fractional integrals namely the riemann liouville and the hadamard fractional integrals into a single form we prove that in most cases we obtain the riemann liouville and the hadamard equivalence just by taking limits when a parameter 1 and 0 respectively

three algorithms for hadamard finite part integrals and fractional derivatives abstract three algorithms for the evaluation of the hadamard finite part integral of the form 1 1 f t 1 t 1 where is a positive non integer are described one algorithm is based on a knowledge of the chebyshev series expansion of f on 1 1 the other two on polynomial interpolations to f at the zeros of tn the chebyshev polynomial of the first kind convergence theorems are given for each algorithm and each algorithm is demonstrated numerically

explicit zeta functions for bosonic and fermionic fields on a non commutative toroidal spacetime explicit formulae for the zeta functions s corresponding to bosonic 2 and to fermionic 3 quantum fields living on a non commutative partially toroidal spacetime are derived formulae for the most general case of the zeta function associated with a quadratic linear constant form in z are obtained they provide the analytical continuation of the zeta functions in relation to the whole complex s plane in terms of series of bessel functions of fast exponential convergence thus being extended chowla selberg formulae as is well known this is the most convenient expression that can be found for the analytical continuation of a zeta function in particular the residua of the poles and their finite parts are explicitly given an important novelty is the fact that simple poles show up at s 0 as well as in other places simple or double depending on the number of compactified non compactified and non commutative dimensions of the spacetime where they had never appeared before this poses a challenge to the zeta function regularization procedure

on the variable order dynamics of the nonlinear wake caused by a sedimenting particle abstract in this work we develop a variable order vo differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid in particular we examine the various force terms in the equation of motion and propose a new form for the history drag acting on the particle we show that the variable order formulation allows for an effective way to express the dynamic transition of the dominant forces over the entire time of the motion of the particle from rest to terminal velocity the use of vo operators also allows us to examine the evolving dynamics of the wake during sedimentation using numerical data from a finite element simulation of a sedimenting particle we first solve for the order of the derivative that returns the correct decay of the history force we then propose a relatively simple expression for the history force that is a function of the reynolds number and particle to fluid density ratio the new history drag expression correlates very well r 2 0 99 with the numerical data for terminal reynolds numbers ranging from 2 5 to 20 and for particle to fluid density ratios of interest in practice 1 10

fractional differential equations of caputo katugampola type and numerical solutions abstract this paper is concerned with a numerical method for solving generalized fractional differential equation of caputo katugampola derivative a corresponding discretization technique is proposed numerical solutions are obtained and convergence of numerical formulae is discussed the convergence speed arrives at o t 1 numerical examples are given to test the accuracy

fractional calculus in the mellin setting and hadamard type fractional integrals abstract the purpose of this paper and some to follow is to present a new approach to fractional integration and differentiation on the half axis r 0 in terms of mellin analysis the natural operator of fractional integration in this setting is not the classical liouville fractional integral i 0 f but j 0 c f x 1 0 x u x c log x u 1 f u du u x 0 for 0 c r the mellin transform of this operator is simply c s m f s for s c it c t r the mellin transform of the associated fractional differentiation operator d 0 c f is similar c s m f s the operator d 0 c f may even be represented as a series in terms of xkf k x k n 0 the coefficients being certain generalized stirling functions sc k of second kind it turns out that the new fractional integral j 0 c f and three further related ones are not the classical fractional integrals of hadamard j mat pure appl ser 4 8 1892 101 186 but far reaching generalizations and modifications of these these four new integral operators are first studied in detail in this paper more specifically conditions will be given for these four operators to be bounded in the space xcp of lebesgue measurable functions f on 0 for c such that 0 u c f u p du u for 1 p ess sup u 0 u c f u for p in particular in the space lp 0 for 1 p connections of these operators with the liouville fractional integration operators are discussed the mellin convolution product in the above spaces plays an important role

some conditions on zeros to avoid step response extrema this note deals with the problem of extrema which may occur in the step response of a linear system with stable real zeros and poles the author gives a simple sufficient condition to avoid extrema using the pole zero configuration of the corresponding transfer function

mellin transform analysis and integration by parts for hadamard type fractional integrals abstract this paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of hadamard in the space xpc of lebesgue measurable functions f on r 0 such that 0 u c f u p du u ess sup u 0 u c f u for c r in particular in the space lp 0 1 p formulas for the mellin transforms of the four hadamard type fractional integral operators are established as well as relations of fractional integration by parts for them

an extension of the chowla selberg formula useful in quantizing with the wheeler de witt equation the two dimensional inhomogeneous zeta function series with homogeneous part of the most general epstein type sigma m n in z am2 bmn cn2 q s is analytically continued in the variable s using zeta function techniques a simple formula is obtained which extends the chowla selberg formula to inhomogeneous epstein zeta functions the new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the wheeler de witt equation in 2 1 dimensional spacetime with the torus topology

finite temperature casimir energy in closed rectangular cavities a rigorous derivation based on a zeta function technique we derive rigorously explicit formulae of the casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by a zeta regularization method we study both the low and high temperature expansions of the free energy in each case we write the free energy as a sum of a polynomial in temperature plus exponentially decay terms we show that the free energy is always a decreasing function of temperature in the cases of massless scalar field with the dirichlet boundary condition and electromagnetic field the zero temperature casimir free energy might be positive in each of these cases there is a unique transition temperature as a function of the side lengths of the cavity where the casimir energy changes from positive to negative when the space dimension is equal to two and three we show graphically the dependence of this transition temperature on the side lengths of the cavity finally we also show that we can obtain the results for a non closed rectangular cavity by letting the size of some directions of a closed cavity go to infinity and we find that these results agree with the usual integration prescription adopted by other authors

zeta function determinant of the laplace operator on the d dimensional ball we present a direct approach for the calculation of functional determinants of the laplace operator on balls dirichlet and robin boundary conditions are considered using this approach formulas for any value of the dimension d of the ball can be obtained quite easily explicit results are presented here for dimensionsd 2 3 4 5 and 6

a technique for choosing zero locations for minimal overshoot an approach is presented to the specification of optimal overshoot controllers when the controller order is fixed and the closed loop system poles are at a fixed location the essential effect of the technique is to pick the best possible locations of the free zeros of the system in terms of minimizing the overshoot the solution is obtained by solving an affine minimax optimization problem an example illustrates how this technique can be used as a design aid when it is necessary to trade off conflicting design requirements such as overshoot and settling time specifications it is shown that the method is not restricted to the deadbeat case but can also be used for any prescribed set of closed loop poles

zeta function regularization is uniquely defined and well hawking s zeta function regularization procedure 1977 is shown to be rigorously and uniquely defined thus putting an end to the spreading lore about different difficulties associated with it basic misconceptions misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method and other analytical procedures are clarified and corrected

a note on katugampola fractional calculus and fractal dimensions abstract the goal of this paper is to study the katugampola fractional integral of a continuous function of bounded variation defined on a closed bounded interval we note that the katugampola fractional integral of a function shares some analytical properties such as boundedness continuity and bounded variation of the function defining it consequently we deduce that fractal dimensions minkowski dimension and hausdorff dimension of the graph of the katugampola fractional integral of a continuous function of bounded variation are one a natural question then arises is whether there exists a continuous function which is not of bounded variation with its graph having fractal dimensions one in the last part of the article we construct a continuous function which is not of bounded variation and for which the graph has fractal dimensions one the construction enunciated herein includes previous constructions found in the recent literature as special cases the article also hints at an upper bound for the upper box dimension of the graph of the katugampola fractional derivative of a continuously differentiable function

simplest equation method for some time fractional partial differential equations with conformable derivative abstract the conformable fractional derivative was proposed by r khalil et al in 2014 which is natural and obeys the leibniz rule and chain rule based on the properties a class of time fractional partial differential equations can be reduced into odes using traveling wave transformation then the simplest equation method is applied to find exact solutions of some time fractional partial differential equations the exact solutions solitary wave solutions periodic function solutions rational function solutions of time fractional generalized burgers equation time fractional generalized kdv equation time fractional generalized sharma tasso olver fsto equation and time fractional fifth order kdv equation 3 1 dimensional time fractional kdv zakharov kuznetsov kdv zk equation are constructed this method presents a wide applicability to solve some nonlinear time fractional differential equations with conformable derivative

non overshooting output tracking of feedback linearisable nonlinear systems the problem of non overshooting output tracking of feedback linearisable single input single output nonlinear systems is considered we present a controller design procedure which makes use of feedback linearisation and global coordinate transformation techniques and is applicable to the cases with a variety of reference inputs and possibly non zero initial conditions for systems with low relative order the sets of feasible controller parameters are constructed and the presented conditions for determining these sets are sufficient and necessary for systems with higher relative order an approach to construct such sets is proposed where the conditions are sufficient two illustrative examples are provided to show the effectiveness of the results

on integral transformations with g function kernels integral transformations t of the formal form where g is a meijer g function are studied on the spaces r of functions f such that results are obtained on the boundedness representation and range of the transformations and on when they have an inverse of the same formal form

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

uniqueness of srb measures for transitive diffeomorphisms on surfaces we give a description of ergodic components of srb measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points for transitive surface diffeomorphisms we prove that there exists at most one srb measure

on the issue of imposing boundary conditions on quantum fields an interesting example of the deep interrelation between physics and mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields this procedure has recently been re examined with care comments on that and previous analysis are provided here together with considerations on the results of the purely mathematical zeta function method in an attempt at clarifying the issue hadamard regularization is invoked in order to fill the gap between the infinities appearing in the qft renormalized results and the finite values obtained in the literature with other procedures

nonovershooting control of strict feedback nonlinear systems a means of obtaining a nonovershooting output tracking response for single input single output siso strict feedback nonlinear systems is introduced with the proposed method arbitrary reference trajectories can be tracked from below for arbitrary initial conditions as long as the initial value of the plant output is strictly below the initial value of the reference trajectory in addition a design is presented for approximately nonovershooting control in the presence of disturbances where the amount of overshoot can be made arbitrarily small by appropriately choosing the control gains finally an output feedback example shows the ability of our approach to ensure arbitrarily small overshoot where the overshoot is caused by the initial condition of the unmeasured part of the state

microlocal analysis and interacting quantum field theories renormalization on physical backgrounds we present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic curved space times we develop a purely local version of the stuckelberg bogoliubov epstein glaser method of renormalization by using techniques from microlocal analysis relying on recent results of radzikowski kohler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved space times we construct time ordered operator valued products of wick polynomials of free fields they serve as building blocks for a local perturbative definition of interacting fields renormalization in this framework amounts to extensions of expectation values of time ordered products to all points of space time the extensions are classified according to a microlocal generalization of steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes as a result we prove that the usual perturbative classification of interacting quantum field theories holds also on curved space times finite renormalizations are deferred to a subsequent paper as byproducts we describe a perturbative construction of local algebras of observables present a new definition of wick polynomials as operator valued distributions on a natural domain and we find a general method for the extension of distributions which were defined on the complement of some surface

complete determination of the singularity structure of zeta functions series of extended epstein type provide examples of non trivial zeta functions with important physical applications the regular part of their analytic continuation is seen to be a convergent or an asymptotic series their singularity structure is completely determined in terms of the wodzicki residue in its generalized form which is proven to yield the residua of all the poles of the zeta function and not just that of the rightmost pole obtainable from the dixmier trace the calculation is a very down to earth application of these powerful functional analytical methods in physics

multidimensional extension of the generalized chowla selberg formula after recalling the precise existence conditions of the zeta function of a pseudodifferential operator and the concept of reflection formula an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous epstein type zeta function of the general form with a the p p matrix of a quadratic form a p vector and q a constant is obtained it is valid on the whole complex s plane is exponentially convergent and provides the residua at the poles explicitly it reduces to the famous formula of chowla and selberg in the particular case p 2 q 0 some variations of the formula and physical applications are considered

on generalized gruss type inequalities for k fractional integrals the aim of the present paper is to investigate some new integral inequalities of gruss type for k riemann liouville fractional integrals from our results new weighted or classical gruss type inequalities have been established for some special cases moreover special cases of the integral inequalities in this paper have been obtained by dahmani and tabharit 2010 in 5

new approach to a generalized fractional integral abstract the paper presents a new fractional integration which generalizes the riemann liouville and hadamard fractional integrals into a single form conditions are given for such a fractional integration operator to be bounded in an extended lebesgue measurable space semigroup property for the above operator is also proved we give a general definition of the fractional derivatives and give some examples

a new algorithm for cauchy principal value and hadamard finite part integrals an algorithm for the approximate evaluation of integrals defined by cauchy principal value or by hadamard finite part has been proposed the convergence of the procedure is proved the stability of the algorithm is considered and some numerical examples are given

some numerical algorithms to evaluate hadamard finite part integrals abstract some algorithms are described for the numerical evaluation of hadamard finite part integrals of type 1 1 f x x t 2 v dx t where v is a jacobi weight convergence results and some numerical examples are given

the microlocal spectrum condition and wick polynomials of free fields on curved spacetimes quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis we discuss a condition on the wave front set for the correspondingn point distributions called microlocal spectrum condition sc on minkowski space this condition is satisfied as a consequence of the usual spectrum condition based on radzikowski s determination of the wave front set of the two point function of a free scalar field satisfying the hadamard condition in the kay and wald sense we construct in the second part of this paper all wick polynomials including the energy momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition

the geometric approach for constructing sinai ruelle bowen measures an important class of physically relevant measures for dynamical systems with hyperbolic behavior is given by sinai ruelle bowen srb measures we survey various techniques for constructing srb measures and studying their properties paying special attention to the geometric push forward approach after describing this approach in the uniformly hyperbolic setting we review recent work that extends it to non uniformly hyperbolic systems

constrained control of input output linearizable systems using control sharing barrier functions abstract control barrier functions cbfs have been used as an effective tool for designing a family of controls that ensures the forward invariance of a set when multiple cbfs are present it is important that the set of controls satisfying all the barrier conditions is non empty in this paper we investigate such a control sharing property for multiple cbfs and provide sufficient and necessary conditions for the property to hold based on that we study the tracking control design problem of an input output linearizable system with multiple time varying output constraints where the output constraints are encoded as cbfs and the barrier conditions are expressed as hard constraints in a quadratic program qp whose feasibility is guaranteed by the control sharing property of the cbfs with the controller generated from the qp the output constraints are always satisfied and the tracking objective is achieved when it is not conflicting with the constraints the effectiveness of our control design method is illustrated by two examples