Open AccessFractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution
Author(s) -
Ndolane Sene
Publication year - 2021
Publication title -
journal of fractional calculus and nonlinear systems
Language(s) - English
Resource type - Journals
ISSN - 2709-9547
DOI - 10.48185/jfcns.v2i1.214
Subject(s) - fractional calculus , uniqueness , mathematics , diffusion equation , mathematical analysis , diffusion , derivative (finance) , operator (biology) , integral equation , heat equation , diffusion process , physics , innovation diffusion , thermodynamics , computer science , biochemistry , chemistry , knowledge management , economy , repressor , gene , transcription factor , financial economics , economics , service (business)
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.