Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel

M. Hosseininia and M.H. Heydari

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 389-399

Abstract: This paper investigates a novel version for the nonlinear 2D telegraph equation involving variable-order (V-O) time fractional derivatives in the Atangana–Baleanu–Caputo sense with Mittag–Leffler non-singular kernel. A meshfree method based on the moving least squares (MLS) shape functions is proposed for the numerical solution of this class of problems. More precisely, the V-O fractional derivatives in this model are approximated by the finite difference scheme at first. Then, the θ-weighted method is utilized to derive a recursive algorithm. Next, the solution of the problem is expanded in terms of the MLS shape functions with undetermined coefficients. Eventually, by substituting this expansion and its partial derivatives into the original equation, solution of the problem in each time step is reduced to the solution of a linear system of algebraic equations. Several numerical examples are investigated to show the applicability, validity and accuracy of the presented method. The achieved numerical results reveal that the established method is high accurate in solving such V-O fractional models.

Keywords: Nonlinear 2D telegraph equation; Moving least squares (MLS) shape functions; Variable-order (V-O); Mittag–Leffler non-singular kernel (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:389-399

DOI: 10.1016/j.chaos.2019.07.015

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