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

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.