Numerical approximations of Atangana–Baleanu Caputo derivative and its application

Swati Yadav, Rajesh K. Pandey and Anil K. Shukla

Chaos, Solitons & Fractals, 2019, vol. 118, issue C, 58-64

Abstract: To solve the problems of non-local dynamical systems, Caputo and Fabrizio proposed a new definition for the fractional derivative. Atangana and Baleanu generalized the Caputo-Fabrizio derivative using the Mittag–Leffler function as the kernel which is both non-singular and non-local. In this paper, we investigate numerical schemes for the Atangana–Baleanu Caputo derivative in two ways and use the same for solving Advection-Diffusion equation whose time derivative is Atangana–Baleanu Caputo derivative. The stability of the schemes is established numerically. Numerical examples are provided to support the theory presented in the paper.

Keywords: Atangana–Baleanu derivative; Fractional Advection-Diffusion equation; Finite difference method (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077918309275
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:118:y:2019:i:c:p:58-64

DOI: 10.1016/j.chaos.2018.11.009

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().