Quasilinearized Semi-Orthogonal B-Spline Wavelet Method for Solving Multi-Term Non-Linear Fractional Order Equations

Can Liu, Xinming Zhang and Boying Wu
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Can Liu: School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Xinming Zhang: School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Boying Wu: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2020, vol. 8, issue 9, 1-15

Abstract: In the present article, we implement a new numerical scheme, the quasilinearized semi-orthogonal B-spline wavelet method, combining the semi-orthogonal B-spline wavelet collocation method with the quasilinearization method, for a class of multi-term non-linear fractional order equations that contain both the Riemann–Liouville fractional integral operator and the Caputo fractional differential operator. The quasilinearization method is utilized to convert the multi-term non-linear fractional order equation into a multi-term linear fractional order equation which, subsequently, is solved by means of semi-orthogonal B-spline wavelets. Herein, we investigate the operational matrix and the convergence of the proposed scheme. Several numerical results are delivered to confirm the accuracy and efficiency of our scheme.

Keywords: multi-term non-linear fractional order equations; fractional integral; Caputo derivative; semi-orthogonal B-spline wavelets; quasilinearization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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