Approximate Solution of Two-Dimensional Linear Systems of Fractional Order Partial Integro-Differential Equations Using Variational Iteration Method

Abstract

The main objective of this paper is to introduce and solve two-dimension linear system of fractional order partial integro-differential equations using the most well-known approximation methods, which is the variational iteration method. After that, the convergence of the derived sequence of iterative approximations to the exact solution is proved, which is must be assumed to be exist according to existence and uniqueness theorem of partial integro-differential equations. Two illustrative examples are considered utilizing the computer software (PTC Mathcad) and then comparison between the exact and the approximate solutions for a test examples are given to show the efficiency and reliability of the proposed method.