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

Youness Assebbane; Mohamed Echchehira; Mohamed Bouaouid; Mustapha Atraoui

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arXiv · 2406.16980

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

Youness Assebbane·Mohamed Echchehira·Mohamed Bouaouid·Mustapha Atraoui

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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.

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Youness Assebbane, Mohamed Echchehira, Mohamed Bouaouid, Mustapha Atraoui. 2024-06-23. A New Method For Solving Fractional And Classical Differential Equations Based On a New Generalized Fractional Power Series. https://arxiv.org/abs/2406.16980

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