The analysis and computation of nabla Mittag–Leffler functions deduced from the frequency domain

Yiheng Wei, Shuaiyu Zhou, Qiang Xu and Feifei Du

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: This paper makes a pioneering contribution to discrete-time fractional calculus by focusing on the nabla Mittag-Leffler function. Motivated by identified limitations in the existing time-domain definition, this work systematically develops a frequency-domain definition. Through rigorous mathematical analysis, a novel framework is established to bridge the gap between time- and frequency-domain representations, with particular emphasis on the carefully constructed initial value conditions. Subsequently, a comprehensive suite of analytic properties is derived, i.e., the numerical relationship and the dynamic behavior. To enable practical applications, three innovative computational schemes are proposed, each accompanied by thorough convergence analysis. The efficacy of our methods is demonstrated through three benchmark numerical examples. These advancements provide new tools for typical applications of nabla fractional order systems.

Keywords: Nabla Mittag–Leffler function; Nabla fractional calculus; Nabla Laplace transform; Dynamic behavior; Numerical computation (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925011701
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:201:y:2025:i:p1:s0960077925011701

DOI: 10.1016/j.chaos.2025.117157

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. ().