A New Method For Solving Fractional And Classical Differential Equations Based On a New Generalized Fractional Power Series

TL;DR

This paper introduces a novel algorithm for solving fractional and classical differential equations using a generalized fractional power series, focusing on the innovative selection of exponents for improved solution expansion.

Contribution

It presents a new generalized fractional power series approach that enhances the solution of differential equations by optimizing exponent choices, differing from traditional methods.

Findings

Effective solution expansion for fractional and classical differential equations.

Improved handling of terms multiplied by powers of t.

New insights into exponent selection for power series solutions.

Abstract

The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE as a generalized power series, shedding light on the choice of the exponent for the monomials. Furthermore, it accommodates situations where terms in the equation are multiplied by $t^{\alpha}$for example. The key contribution is how the exponents for these terms are chosen, which is different from traditional methods.