global existence theory and chaos control of fractional differential equations in this paper the initial value problem for a class of fractional differential equations is discussed which generalizes the existent result to a wide class of fractional differential equations also the theoretical result established in the paper ensures the validity of chaos control of fractional differential equations in particular feed back control of chaotic fractional differential equation is theoretically investigated and the fractional lorenz system as a numerical example is further provided to verify the analytical result

a cauchy problem for some fractional abstract differential equation with non local conditions abstract we discuss in this paper the existence and uniqueness of solutions to the cauchy problem for the fractional differential equation with non local conditions d q x t f t x t t 0 t x 0 g x x 0 where 0 q 1 in a banach space we use classical tools from functional analysis to obtain the results

fractional variational homotopy perturbation iteration method and its application to a fractional diffusion equation in this paper we use the fractional variational homotopy perturbation iteration method fvhpim with modified riemann liouville derivative to solve a time fractional diffusion equation using this method a rapid convergent sequence tending to the exact solution of the equation can be obtained to show the efficiency of the considered method some numerical examples are presented

a study on the mild solution of impulsive fractional evolution equations this paper is concerned with the formula of mild solutions to impulsive fractional evolution equation for linear fractional impulsive evolution equations 8 25 27 30 31 described mild solution as integrals over t k t k 1 k 1 2 m and 0 t1 on the other hand in 26 28 29 their solutions were expressed as integrals over 0 t however it is still not clear what are the correct expressions of solutions to the fractional order impulsive evolution equations in this paper firstly we prove that the solutions obtained in 8 25 27 30 31 are not correct secondly we present the right form of the solutions to linear fractional impulsive evolution equations with order 0 1 and 1 2 respectively finally we show that the reason that the solutions to an impulsive ordinary evolution equation are not distinct

existence results for fractional order functional differential equations with impulse in this paper we use the analytic semigroup theory of linear operators and the fixed point method to prove the existence of mild solutions for the semilinear fractional order functional differential equations with impulse in a banach space

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

existence of the mild solution for fractional semilinear initial value problems abstract in this paper we will study the existence and uniqueness of mild solution for the semilinear initial value problem of non integer order u t a u t f t u t g u t s u t where 0 1 and f t u t g u t s u t is a given function

the existence of mild solutions for impulsive fractional partial differential equations abstract this paper is concerned with the existence of mild solutions for a class of impulsive fractional partial semilinear differential equations some errors in mophou 2010 2 are corrected and some previous results are generalized

fractional cauchy problems with almost sectorial operators this paper concerns the abstract cauchy problem of fractional evolution equations with almost sectorial operators the suitable mild solutions of evolution equations with riemann liouville derivative and caputo derivative are introduced respectively the existence theorems of mild solutions of cauchy problems are established the results obtained here improve and generalize some known results finally an example is given for demonstration

weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations abstract this paper is concerned with the existence and uniqueness of weighted pseudo almost automorphic mild solution to the semilinear fractional equation d t u t au t d t 1 f t u t bu t t r 1 2 where a is a linear densely defined operator of sectorial type on a complex banach space x and b is a bounded linear operator defined on x under the assumption of uniformly continuity on f we establish a composition of weighted pseudo almost automorphic in a general banach space and obtain existence results by means of banach contraction mapping the results obtained are utilized to study the existence and uniqueness of a weighted pseudo almost automorphic solution to fractional diffusion wave equation with dirichlet conditions

on recent developments in the theory of abstract differential equations with fractional derivatives abstract this note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives we show that the existence results in agarwal et al 2009 1 belmekki and benchohra 2010 2 darwish et al 2009 3 hu et al 2009 4 mophou and n guerekata 2009 6 7 mophou 2010 8 9 muslim 2009 10 pandey et al 2009 11 rashid and el qaderi 2009 12 and tai and wang 2009 13 are incorrect since the considered variation of constant formulas is not appropriate in this note we also consider a different approach to treat a general class of abstract fractional differential equations

existence and uniqueness of mild solutions to impulsive fractional differential equations this paper is concerned with the existence and uniqueness of a mild solution to impulsive fractional semilinear differential equations the results are obtained by means of fixed point methods we also give an example of such problems

functional interval observer for discrete time systems with disturbances abstract this paper further investigates the design problem of the functional interval observer for discrete time systems with disturbances two methods are given to design functional interval observers given monotone system theory a luenberger like functional interval observer is constructed and sufficient conditions are achieved by sylvester equations in the first method the second approach is known as the two step method an h functional observer of the system is presented by the h technique and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy the above methods are applied to two examples for comparison and to show the correctness

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions this paper investigates the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order email protected 1 2 our results are based on some standard fixed point theorems some examples are presented to illustrate the main results

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

existence and uniqueness of mild solutions for abstract delay fractional differential equations in this paper by means of solution operator approach and contraction mapping theorem the existence and uniqueness of mild solutions for a class of abstract delay fractional differential equations are obtained

solutions to the cauchy problem for differential equations in banach spaces with fractional order in this paper we use the monotone iterative technique combined with cone theory to investigate the existence of solutions to the cauchy problem for caputo fractional differential equations in banach spaces new existence theorems are obtained for the case of a cone p being normal and fully regular respectively moreover two examples are given to illustrate the abstract results

controllability for a class of fractional order neutral evolution control systems abstract in this paper we consider a class of fractional neutral control systems governed by abstract nonlinear fractional neutral differential equations this paper deals with the exact controllability for fractional differential neutral control systems first we establish a new set of sufficient conditions for the controllability of nonlinear fractional systems by using a fixed point analysis approach further we extend the result to study the controllability concept with nonlocal conditions in particular the controllability of nonlinear systems is established under the natural assumption that the associated linear control system is exactly controllable