Boubaker operational matrix method for fractional Emden--Fowler problem

Abdelkrim Bencheikh ; Lakhdar Chiter

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 3, pp. 357-369.

Résumé

In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the formulation for its fractional derivative operational matrix. However, the use of Boubaker polynomials is most recent, and has not been discussed in the literature, since most of application areas of these polynomials require orthogonal polynomials, and here we have introduced it for the first time. The operational matrixof the Caputo fractional derivative tool converts the Emden–Fowler equation to a system of algebraic equations whose solutions are easy to compute. Numerical examples are examined to prove the validity and the effectiveness of the proposed method.

Détail

Keywords: Boubaker polynomials, operational matrix of fractional derivatives, collocation method, fractional Emden–Fowler type equations.

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