A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

N H Tuan; R M Ganji; H Jafari

doi:10.1016/j.cjph.2020.08.019

A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

Chin J Phys. 2020 Dec:68:308-320. doi: 10.1016/j.cjph.2020.08.019. Epub 2020 Sep 1.

Authors

N H Tuan¹, R M Ganji², H Jafari^{3

4

5}

Affiliations

¹ Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam.
² Department of Mathematics, University of Mazandaran, Babolsar, Iran.
³ Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.
⁴ Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam.
⁵ Department of Mathematical Sciences, University of South Africa, UNISA, 0003, South Africa.

Abstract

In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples.

Keywords: Fractional Newell-Whitehead-Segel equations; Fractional rheological models; New fractional derivatives; Non-local kernel; Non-singular kernel; The spectral collocation method.