A numerical method for solving fractional delay differential equations based on the operational matrix method. (June 2021)

• Record Type: Journal Article
• Authors: Syam, Muhammed I.; Sharadga, Mwaffag; Hashim, I.
• Is Part Of: Chaos, solitons and fractals. Volume 147(2021)
• Publication Date: 2021-06
• Subjects: Fractional delay differential equation -- Operational matrix -- Caputo derivative; 76A05 -- 76W05 -- 76Z99 -- 65L05; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110977
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We generate orthogonal basis for the domain of the solution. Then, we derived the operational matrix technique to solve the first order fractional delay equation. The error is very small in our approximation. The solution profile is increasing as μ is increasing in Example 1 and 2 is increasing as μ is increasing. This appears from Figures (1) and (2). The results show that the proposed method is accurate for such problems. Abstract: The Modified Operational Matrix method (MOMM) has proved to be a reliable and efficient algorithm for solving fractional delay equations. However, no convergence results are known in the literature. The aim of this paper is to derive the MOMM and to show its efficiency. Numerical examples are studied to illustrate the efficiency of the proposed method.