INNOVATIVE TECHNIQUES FOR SOLVING FRACTIONAL INTEGRO DIFFERENTIAL EQUATIONS USING ADOMIAN DECOMPOSITION

Abstract

Fractional integro-differential equations (FIDEs) are integral in modeling complex systems in science and engineering due to their ability to capture memory and hereditary properties. However, solving such equations analytically remains a significant challenge. This paper presents innovative techniques for solving FIDEs using the Adomian Decomposition Method (ADM). By integrating modifications such as the use of Caputo and Riemann–Liouville fractional derivatives, convergence acceleration, and adaptive decomposition strategies, the method is enhanced to tackle a wide range of linear, nonlinear, and multiterm FIDEs efficiently. Numerical examples are provided to illustrate the accuracy and robustness of the proposed techniques. In addition, convergence behavior and error bounds of the proposed ADM variants are theoretically analyzed and numerically validated. A comprehensive theoretical and numerical investigation is conducted, highlighting the advantages, limitations, and potential for future research in this domain.