# American Institute of Mathematical Sciences

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## Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution

 Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Laboratoire Lmdan, BP 5683 Dakar Fann, Sénégal

* Corresponding author: Ndolane Sene

Received  March 2019 Revised  May 2019 Published  December 2019

In this paper, we propose the approximate solution of the fractional diffusion equation described by a non-singular fractional derivative. We use the Atangana-Baleanu-Caputo fractional derivative in our studies. The integral balance methods as the heat balance integral method introduced by Goodman and the double integral method developed by Hristov have been used for getting the approximate solution. In this paper, the existence and uniqueness of the solution of the fractional diffusion equation have been provided. We analyze the impact of the fractional operator in the diffusion process. We represent graphically the approximate solution of the fractional diffusion equation.

Citation: Ndolane Sene. Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020173
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##### References:
Approximate solutions of diffusion equation, $\alpha = 0.5$
Approximate solutions of diffusion equation, different $\alpha$ and $t = 0.6$