Title: Stable RBF-RA method for solving fuzzy fractional kinetic equation

Authors: Hossein Jafari; Behshid Fakhr Kazemi

Addresses: Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran; Department of Mathematical Sciences, University of South Africa, P.O. Box 392, UNISA, 0003, South Africa; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 110122, Taiwan ' Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

Abstract: The direct method based on the flat radial basis functions (RBFs) for obtaining numerical solution of differential equations is highly ill-conditioned. Therefore, many studies have been dedicated to overcome this ill-conditioning by using different techniques. Here, the RBF algorithm based on vector-valued rational approximations is utilised to obtain the numerical solution of fuzzy fractional differential equations. This stable method can be applied with any sort of smooth RBF easily and accurately. To illustrate the accuracy and stability of the presented algorithm, we focus on solving the kinetic model with fuzzy fractional derivative.

Keywords: RBFs; radial basis functions; rational approximation; kinetic fuzzy fractional model; shape parameter; Caputo-fuzzy fractional derivative; vector-valued rational approximation.

DOI: 10.1504/IJDSDE.2022.123411

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.2, pp.163 - 182

Accepted: 03 Jul 2020
Published online: 20 Jun 2022 *

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