Kernel-based approximation of variable-order diffusion models

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.