ψ-Haar wavelets method for numerically solving fractional differential equations

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.