Journal
CHAOS SOLITONS & FRACTALS
Volume 99, Issue -, Pages 171-179Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2017.04.008
Keywords
Caputo-Fabrizio derivative; Exponential decay-law; Exponential time differencing; Finite difference method; Fractional nonlinear PDEs; Numerical simulations; Riemann-Liouville definition
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This paper considers the Caputo-Fabrizio derivative in Riemann-Liouville sense for the spatial discretization fractional derivative. We formulate two notable exponential time differencing schemes based on the Adams-Bashforth and the Runge-Kutta methods to advance the fractional derivatives in time. Our approach is tested on a number of fractional parabolic differential equations that are of current and recurring interest, and which cover pitfalls and address points and queries that may naturally arise. The effectiveness and suitability of the proposed techniques are justified via numerical experiments in one and higher dimensions. (C) 2017 Elsevier Ltd. All rights reserved.
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