We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...

In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods. General Terms Numerical solutions, Fractional integro-differential equations.

A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous sub-diffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and conv...

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

Correspondence: [email protected] Department of Mathematics, Faculty of Science, Guelma University Guelma, Algeria Abstract In this article, sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus, resolvent operators, and ...

In this paper, we use the theory of resolvent operators, the fractional powers of operators, fixed point technique and the Gelfand–Shilov principle to establish the existence and uniqueness of local mild and then local classical solutions of a class of nonlinear fractional evolution integro-differential systems with nonlocal conditions in Banach space. As an application that illustrates the abs...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...