A numerical method for solving fractional differential equations

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.

Citation

ul Abdeen, Z. and Rehman, M.u. (2019), "A numerical method for solving fractional differential equations", Engineering Computations, Vol. 36 No. 2, pp. 551-568. https://doi.org/10.1108/EC-07-2018-0302