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

https://doi.org/10.48185/jfcns.v2i1.214

Authors

Keywords:

Fractional diffusion equations, Approximate solutions, Atangana-Baleanu, Fractional derivative operator

Abstract

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.

Published

2021-06-29

How to Cite

Sene, N. . (2021). Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution. Journal of Fractional Calculus and Nonlinear Systems, 2(1), 60–75. https://doi.org/10.48185/jfcns.v2i1.214