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.
Highlights
IntroductionFractional calculus has received many attractions. This attraction is due to the various fractional derivatives used in the fields of fractional calculus
Nowadays, fractional calculus has received many attractions
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
Summary
Fractional calculus has received many attractions. This attraction is due to the various fractional derivatives used in the fields of fractional calculus. Hristov started the physical interpretations of the fractional diffusion equation described by the Atangana Baleanu fractional derivative in Caputo sense in [18]. We come with a new approximate solution of the fractional diffusion equation described by the Atangana Baleanu fractional derivative in Caputo sense. The main contribution of this study is to give a potential physical interpretation of the fractional diffusion equation described by the Atangana-Baleanu fractional derivative in Caputo sense.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Fractional Calculus and Nonlinear Systems
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
