Adomian decomposition method (ADM) is applied to approximately solve stochastic fractional integrodifferential equations involving nonlocal initial condition. The convergence of the ADM for the considered problem is proved. The mean square error between approximate solution and accurate solution is also given. [Mahmoud M. El-Borai, M.A.Abdou, Mohamed Ibrahim M. Youssef. On Adomian’s Decompositi...

In this paper, homotopy perturbation method is applied to solve non-linear Fredholm integrodifferential equations of fractional order. Examples are presented to illustrate the ability of the method. The results reveal that the proposed methods very effective and simple and show that this method can be applied to the non-fractional cases.

In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in the Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration f...

In this paper, the existence of mild solutions for the fractional differential equations of neutral type with infinite delay is obtained under the conditions in respect of the Kuratowski’s measure of noncompactness. As an application, the existence of mild solution for some integrodifferential equation is obtained. keywords: fractional differential equation, neutral differential equation, mild ...

Integrodifferential equations arise in many fields of science and engineering such as fluid dynamics, biological models, and chemical kinetics. A detailed investigation of integrodifferential equations and their solution via the Laplace transform method can be found in the work of Burton (1983). Recently, fractional integrodifferential equations have been used to model various physical phenomen...

The aim of the present paper is to establish the existence, uniqueness and boundedness of solutions to the nonlocal fractional integrodifferential equations in Banach spaces. Mathematics Subject Classification: 26A33, 34K12, 34A40, 35B60, 45N05, 45G15

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a conc...

This paper addresses the issue of approximate controllability for a class of control systemwhich is represented bynonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results ...