This article is cited in 1 paper

Differential Equations and Mathematical Physics

Khalouta transform via different fractional derivative operators

A. Khalouta

Université Ferhat Abbas de Sétif 1, Sétif, 19000, Algeria

Abstract: 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.

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

UDC: 519.642.2

MSC: 34A08, 35A22, 33E12, 35C10

Received: February 2, 2024
Revised: September 20, 2024
Accepted: September 27, 2024
First online: November 12, 2024

Language: English

DOI: 10.14498/vsgtu2082

Bibliographic databases:

• 
• 
• 
•