ψ -Haar wavelets method for numerically solving fractional differential equations
ISSN: 0264-4401
Article publication date: 12 August 2020
Issue publication date: 8 February 2021
Abstract
Purpose
The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative.
Design/methodology/approach
An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems.
Findings
The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples.
Research limitations/implications
The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity.
Originality/value
Engineers and applied scientists may use the present method for solving fractional models appearing in applications.
Keywords
Acknowledgements
The authors are grateful to the anonymous reviewers for their valuable comments which led to the significant improvement of the manuscript.
Citation
Ali, A., Minamoto, T., Saeed, U. and Rehman, M.U. (2021), "
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited