ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION

Umair Ali, Muhammad Naeem, Farah Aini Abdullah, Miao-Kun Wang and Fouad Mohammad Salama
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Umair Ali: Department of Applied Mathematics and Statistics, Institute of Space Technology, P. O. Box 2750, Islamabad 44000, Pakistan‡School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
Muhammad Naeem: ��Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
Farah Aini Abdullah: ��School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
Miao-Kun Wang: �Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R. China¶Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University Hangzhou, Zhejiang 211121, P. R. China
Fouad Mohammad Salama: ��Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-14

Abstract: This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann–Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme.

Keywords: Implicit Scheme; Variable-Order Fractional Modified Sub-Diffusion Equation; Stability; Convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402538

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