Fractional Emden-Fowler Problem by Operational Matrix Based on Legendre Polynomials

Résumé

This paper introduces the singular Emden-Fowler equation of fractional order and proposes a computational method to facilitate its numerical solution. To approximate its solutions, Legendre polynomials are employed, along with the formulation of the fractional derivative operational matrix. By utilizing the operational matrix associated with the Caputo fractional derivative, the problem is transformed into a system of algebraic equations, making the computations straightforward and efficient. Several numerical examples are provided to demonstrate the accuracy and effectiveness of the proposed method in obtaining both approximate and reliable solutions