Ψ-Haar wavelets method for numerically solving fractional differential equations. Issue 2 (12th August 2020)

• Record Type: Journal Article
• Authors: Ali, Amjid; Minamoto, Teruya; Saeed, Umer; Rehman, Mujeeb Ur
• Is Part Of: Engineering computations. Volume 38:Issue 2(2021)
• Page Start: 1037
• Page End: 1056
• Publication Date: 2020-08-12
• Subjects: Convergence -- ψ-Caputo fractional integral and derivative -- ψ-Haar wavelets operational matrices -- Collocation points -- Generalized fractional differential equations -- Quasi linearization; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-01-2020-0050
• Languages: English
• ISSNs: 0264-4401

Abstract

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.