Analytical solutions to the advection-diffusion equation with the Atangana-Baleanu derivative over a finite domain | Zendy

Derya Avcı | Zendy; Aylіn Yetіm | Zendy

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Analytical solutions to the advection-diffusion equation with the Atangana-Baleanu derivative over a finite domain

Author(s) -

Derya Avcı,

Aylіn Yetіm

Publication year - 2018

Publication title -

balıkesir üniversitesi fen bilimleri enstitüsü dergisi

Language(s) - English

Resource type - Journals

eISSN - 2536-5142

pISSN - 1301-7985

DOI - 10.25092/baunfbed.487074

Subject(s) - mathematics , mathematical analysis , laplace transform , cauchy distribution , fourier transform , advection , transformation (genetics) , diffusion , diffusion equation , domain (mathematical analysis) , derivative (finance) , physics , biochemistry , chemistry , gene , thermodynamics , economy , financial economics , economics , service (business)

In this paper, an advection-diffusion equation with Atangana-Baleanu derivative is considered. Cauchy and Dirichlet problems have been described on a finite interval. The main aim is to scrutinize the fundamental solutions for the prescribed problems. The Laplace and the finite sin-Fourier integral transformation techniques are applied to determine the concentration profiles corresponding to the fundamental solutions. Results have been obtained as linear combinations of one or bi-parameter Mittag-Leffler functions. Consequently, the effects of the fractional parameter and drift velocity parameter on the fundamental solutions are interpreted by the help of some illustrative graphics.

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