Existence theory and semi-analytical study of non-linear Volterra fractional integro-differential equations

Abstract

In this article, we investigate the semi-analytic solutions of non-linear Volterra fractional integro-differential equations by using Laplace Adomian decomposition method. We discuss the method in general and provide examples for the illustration purpose. Moreover, we give existence and uniqueness result for the solutions using Banach contraction principle as tool. Also we provide some results for the convergence of Laplace Adomian decomposition technique. The results in this work show that the method of Laplace Adomian decomposition is an effective tool for the solutions of Volterra fractional integro-differential equations.