Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense

Kolade M. Owolabi and Abdon Atangana

Chaos, Solitons & Fractals, 2017, vol. 99, issue C, 171-179

Abstract: 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.

Keywords: Caputo–Fabrizio derivative; Exponential decay-law; Exponential time differencing; Finite difference method; Fractional nonlinear PDEs; Numerical simulations; Riemann–Liouville definition (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:99:y:2017:i:c:p:171-179

DOI: 10.1016/j.chaos.2017.04.008

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