A Numerical Method for Fractional Differential Equations with New Generalized Hattaf Fractional Derivative. (30th May 2022)

• Record Type: Journal Article
• Authors: Hattaf, Khalid; Hajhouji, Zakaria; Ait Ichou, Mohamed; Yousfi, Noura
• Other Names: Jajarmi Amin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2022(2022)
• Publication Date: 2022-05-30
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2022/3358071
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Nowadays, fractional derivative is used to model various problems in science and engineering. In this paper, a new numerical method to approximate the generalized Hattaf fractional derivative involving a nonsingular kernel is proposed. This derivative included several forms existing in the literature such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. The new proposed method is based on Lagrange polynomial interpolation, and it is applied to solve linear and nonlinear fractional differential equations (FDEs). In addition, the error made during the approximation of the FDEs using our proposed method is analyzed. By comparing the approximate and exact solutions, it is noticed that the new numerical method is very efficient and converges very quickly to the exact solution. Furthermore, our proposed numerical method is also applied to nonlinear systems of FDEs in virology.