A Numerical approach of fractional advection-diffusion equation with Atangana–Baleanu derivative

H. Tajadodi

Chaos, Solitons & Fractals, 2020, vol. 130, issue C

Abstract: In the current paper, a new approach is applied to solve time fractional advection-diffusion equation. The utilized fractional derivative operator is the Atangana–Baleanu (AB) derivative in Caputo sense. The mentioned fractional derivative involves the Mittag–Leffler function as the kernel that is both non-singular and non-local. A new operational matrix of AB fractional integration is obtained for the Bernstein polynomials (Bps). By applying the aforesaid matrix, the considered problems are reduced to a system of equations. The approximate solution is derived by solving the yielded system. Also, the error bound is studied. The obtained results show that the applied scheme is simple and powerful tool in finding numerical solutions of fractional equations.

Keywords: Advection-Diffusion; Atangana-Baleanu derivative; Operational matrix; Bernstein polynomials (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919304783

DOI: 10.1016/j.chaos.2019.109527

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