Numerical simulation of nonlinear fractional integrodifferential equations of Volterra type via power series expansion

Abstract

In this article, an effective recent analytical treatment is presented to solve a certain class of nonlinear fractional integrodifferential equations of Volterra type based on the residual error functions.  The solution methodology of the fractional power series (FPS) approach is to replace the n-term truncated solution by generalized fractional power series to minimize the residual error function through the derivation of those functions under the Caputo concept.  Anyhow, the approximate solution is obtained directly in a rapidly convergent fractional power series without needed to linearization, perturbation, or discretization.  Numerical examples are performed to show the validity and reliability of the FPS method.  Numerical analysis of the results indicates that the RPS approach is simple, efficient and systematic tool in solving fractional nonlinear issues arising in applied mathematics, physics and engineering.