A numerical method for solving fractional differential equations

• Published in: Engineering computations Vol. 36; no. 2; pp. 551 - 568
• Main Authors: ul Abdeen, Zain, Rehman, Mujeeb ur
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 11.03.2019; Emerald Group Publishing Limited
• Subjects: Boundary value problems; Fractional calculus; Integral equations; Linearization; Nonlinear differential equations; Nonlinear equations; Numerical analysis; Numerical methods; Quadratures; Robustness (mathematics); Quadrature method; Fractional differential equations; Numerical solutions; Caputo derivative
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-07-2018-0302

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.