Fractional diffusions arise in the study of models from population dynamics. In this paper, we derive a class of integro-differential reactiondiffusion equations from simple principles. We then prove an approximation result for the first eigenvalue of linear integro-differential operators of the fractional diffusion type, and we study from that the dynamics of a population in a fragmented envir...

The object of this paper is to solve a fractional integro-differential equation involving a generalized Lauricella confluent hypergeometric function in several complex variables and the free term contains a continuous function f (τ). The method is based on certain properties of fractional calculus and the classical Laplace transform. A Cauchy-type problem involving the Caputo fractional derivat...

This study aims to solve the most general form of linear mixed Volterra-Fredholm integro-differential equations multi-fractional order in Caputo sense (MV-FIFDEs), which is solved by using orthogonal generalized Bernstein’s polynomial expansion with collocation and moment discrete weighted residual method under suitable conditions; then, Clenshaw-Curtis formula applied approximate integral term...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

Abstract The Cauchy problem of a time-space fractional partial differential equation which has as particular cases the Klein-Gordon equation, generalized expression heat and two apparently unexplored integro-differential equations in context physics, is proposed solved for delta initial condition. Series H-Fox functions are obtained solution.

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally examples are given to illustrate the analytical findings. Mathematics Subject Classification(2010): 34A08, 1...

Abstract: This paper studies the existence of the mild solution for the neutral fractional integro-differential equation with nonlocal initial conditions in a Banach space. We obtain the sufficient condition for the existence results via fixed point theorem and approximate technique without assuming noncompactness or Lipschitz continuity of the nonlocal functions. We give an example for explain...