Khalouta transform via different fractional derivative operators

A. Khalouta

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 3, pp. 407-425

Résumé

Recently, the author defined and developed a new integral transform namely the Khalouta transform, which is a generalization of many well-known integral transforms. The purpose of this paper is to extend this new integral transform to include different fractional derivative operators. The fractional derivatives are described in the sense of Riemann–Liouville, Liouville–Caputo, Caputo–Fabrizio, Atangana–Baleanu–Riemann–Liouville, and Atangana–Baleanu–Caputo. Theorems dealing with the properties of the Khalouta transform for solving fractional differential equations using the mentioned fractional derivative operators are proven. Several examples are presented to verify the reliability and effectiveness of the proposed technique. The results show that the Khalouta transform is more efficient and useful in dealing with fractional differential equations.

Détail

Keywords: fractional differential equations, Riemann–Liouville derivative, Liouville–Caputo derivative, Caputo–Fabrizio derivative, Atangana–Baleanu–Riemann–Liouville derivative, Atangana–Baleanu–Caputo derivative
Mots-clés : Khalouta transform, exact solution