Analytical Solutions for Riemann-Liouville Fractional Operators Using a Generalized Power Series Framework

Abstract

In this paper, we propose a general form of the power series method to solve non-trivial fractional

differential equations within the Riemann-Liouville framework . The proposed methodology extends

and refines conventional series techniques, effectively overcoming their principal limitations. A rigorous

theoretical foundation underpinning the approach is established, encompassing essential theorems and

a comprehensive convergence analysis that guarantees its reliability. The practical efficacy of the

method is demonstrated through its application to a variety of fractional models, where it is shown to

yield accurate solutions and exhibit performance advantages over some existing schemes