A numerical method based on Haar wavelets for the Hadamard-type fractional differential equations

Abstract

Purpose

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear Hadamard-type fractional differential equations.

Design/methodology/approach

The aim of this paper is to develop a numerical scheme for numerical solutions of Hadamard-type fractional differential equations. The classical Haar wavelets are modified to align them with Hadamard-type operators. Operational matrices are derived and used to convert differential equations to systems of algebraic equations.

Findings

The upper bound for error is estimated. With the help of quasilinearization, nonlinear problems are converted to sequences of linear problems and operational matrices for modified Haar wavelets are used to get their numerical solution. Several numerical examples are presented to demonstrate the applicability and validity of the proposed method.

Originality/value

The numerical method is purposed for solving Hadamard-type fractional differential equations.

Citation

ul Abdeen, Z. and Rehman, M.u. (2022), "A numerical method based on Haar wavelets for the Hadamard-type fractional differential equations", Engineering Computations, Vol. 39 No. 3, pp. 943-964. https://doi.org/10.1108/EC-04-2021-0223