Modified fractional difference operators defined using Mittag-Leffler kernels

Date

2022

Authors

Mohammed, Pshtiwan Othman
Srivastava, H.M.
Baleanu, Dumitru
Abualnaja, Khadijah M.

Journal Title

Journal ISSN

Volume Title

Publisher

Symmetry

Abstract

The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maintaining the safe operation of kernels and symmetry of discrete delta and nabla distribution. In their discrete version, the generalized or modified forms of various operators of fractional calculus are becoming increasingly important from the viewpoints of both pure and applied mathematical sciences. In this paper, we present the discrete version of the recently modified fractional calculus operator with the Mittag-Leffler-type kernel. Here, in this article, the expressions of both the discrete nabla derivative and its counterpart nabla integral are obtained. Some applications and illustrative examples are given to support the theoretical results.

Description

Keywords

discrete fractional calculus, discrete Atangana-Baleanu fractional differences, discrete Liouville-Caputo operator, discrete Mittag-Leffler kernels

Citation

Mohammad, P., Srivastava, H., Baleanu, D., & Abualnaja, K. (2022). “Modified fractional difference operators defined using Mittag-Leffler kernels.” Symmetry, 14(8), 1519. https://doi.org/10.3390/sym14081519