Certain new models of the multi space-fractional Gardner equation

A.A. Alderremy, Khaled M. Saad, Praveen Agarwal, Shaban Aly and Shilpi Jain

Physica A: Statistical Mechanics and its Applications, 2020, vol. 545, issue C

Abstract: In this paper, we study an accurate numerical method for solving the multi space-fractional Gardner equation (MSFGE) with the Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional derivatives where the space-fractional terms are under the sense of Caputo. To the best knowledge of the reader, we are first to use the spectral collocation method based on the third Chebyshev approximations to reduced the multi space-fractional Gardner equation to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them via the finite difference method (FDM). By computing the absolute errors we present the effectiveness and accuracy of the proposed methods. The present paper investigates the dynamics of Gardner Equation by considering two fractional operators that is the Caputo–Fabrizio and Atangana–Baleanu, this is entirely new idea by using the two operators on a Gardner equation. Our results prove that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.

Keywords: Fractional Caputo–Fabrizio derivative; ABC-fractional derivative; Mittag-Leffler kernel; Chebyshev polynomials approximation (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321181

DOI: 10.1016/j.physa.2019.123806

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