A numerical method for solving fractional differential equations. Issue 2 (18th January 2019)

• Record Type: Journal Article
• Authors: ul Abdeen, Zain; Rehman, Mujeeb ur
• Is Part Of: Engineering computations. Volume 36:Issue 2(2019)
• Page Start: 551
• Page End: 568
• Publication Date: 2019-01-18
• Subjects: Numerical solutions -- Caputo derivative -- Fractional differential equations -- Quadrature method; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2018-0302
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this paper is to present a computational technique based on Newton–Cotes quadrature rule for solving fractional order differential equation. Design/methodology/approach: The numerical method reduces initial value problem into a system of algebraic equations. The method presented here is also applicable to non-linear differential equations. To deal with non-linear equations, a recursive sequence of approximations is developed using quasi-linearization technique. Findings: The method is tested on several benchmark problems from the literature. Comparison shows the supremacy of proposed method in terms of robust accuracy and swift convergence. Method can work on several similar types of problems. Originality/value: It has been demonstrated that many physical systems are modelled more accurately by fractional differential equations rather than classical differential equations. Therefore, it is vital to propose some efficient numerical method. The computational technique presented in this paper is based on Newton–Cotes quadrature rule and quasi-linearization. The key feature of the method is that it works efficiently for non-linear problems.