Kernel-based approximation of variable-order diffusion models
by Marjan Uddin; Muhammad Awais
International Journal of Computing Science and Mathematics (IJCSM), Vol. 16, No. 2, 2022

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.

Online publication date: Mon, 19-Dec-2022

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