Title: Kernel-based approximation of variable-order diffusion models

Authors: Marjan Uddin; Muhammad Awais

Addresses: Department of Basic Sciences, University of Engineering and Technology Peshawar, 25000, Pakistan ' Department of Basic Sciences, University of Engineering and Technology Peshawar, 25000, Pakistan

Abstract: In this paper, a numerical scheme is constructed that is based on radial basis functions (RBF) and the Coimbra variable time fractional derivative of order 0 < α(t, x) ≤ 1. The derivative due to Coimbra can efficiently model a dynamical system whose fractional order behaviour varies with time as well as space. The stability and convergence of the RBF-based numerical scheme are discussed and the developed numerical scheme is validated for various 1D and 2D anomalous diffusion models with different fractional variable orders either a function of t or x . The accuracy and efficiency of the numerical scheme are achieved by comparing the results of available results in the literature.

Keywords: RBF; radial basis functions; variable order; fractional order; anomalous diffusion; numerical approximation; Coimbra derivative.

DOI: 10.1504/IJCSM.2022.127808

International Journal of Computing Science and Mathematics, 2022 Vol.16 No.2, pp.159 - 169

Received: 26 Mar 2020
Accepted: 26 Jul 2021
Published online: 19 Dec 2022 *

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