A New Approach for Solving Fractional Differential Equations Incorporating Ramadan Group Transform and Machine Learning

Abstract

Listen

Translate article

This paper examines various types of fractional differential equations using fractional calculus methods. It extends the classical Frobenius method and introduces key theorems that apply the Ramadan Group transform and other techniques. Additionally, the research incorporates machine learning, specifically neural networks, to solve these equations. The paper demonstrates that machine learning can enhance the solution process through data generation, model design, and optimization. Examples provided illustrate how combining traditional methods with machine learning can effectively solve fractional differential equations.