MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION

Madiha Shafiq (), Farah Aini Abdullah, Muhammad Abbas (), Ahmed Sm Alzaidi () and Muhammad Bilal Riaz ()
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Madiha Shafiq: Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Farah Aini Abdullah: School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Ahmed Sm Alzaidi: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Muhammad Bilal Riaz: Institute of Applied Mathematics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, 80-233 Gdańsk, Poland

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-25

Abstract: The purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic B-spline functions for discretization along temporal and spatial grids, respectively. To ensure that the error does not amplify during computational process, stability analysis is performed. The described algorithm is second-order convergent along time and space directions. The computational competence of the scheme is tested through some numerical examples. The results reveal that the current scheme is reasonably efficient and reliable to be used for solving the subject problem.

Keywords: Diffusion Equation; Spline Interpolation; Caputo–Fabrizio Fractional Derivative; Cubic B-Spline Functions; Stability; Finite Difference Formulation; Convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402708

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