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

2024/06/23 by Youness Assebbane, Assebbane, Youness, Mohamed Echchehira +5
Mathematics · #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2406.16980

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^αfor example. The key contribution is how the exponents for these terms are chosen, which is different from traditional methods.

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