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