Discrete Prabhakar fractional difference and sum operators

Pshtiwan Othman Mohammed, Thabet Abdeljawad and Faraidun Kadir Hamasalh

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: The Prabhakar fractional operator is commonly acclaimed as the queen model of fractional calculus. Our aim in this article is to introduce the notion of the discrete Prabhakar fractional operator with discrete generalized Mittag-Leffler function in the kernel, in the context of discrete fractional calculus. Also, we examine some relationships between our new model with the discrete Atangana–Baleanu fractional model implemented by Abdeljawad. By doing these relationships, we can find a few interesting properties of both, as well as of the original discrete Atangana–Baleanu fractional models and their iterated forms. We can confirm that this is the first paper introducing and studying the discrete Prabhakar fractional operators in the context of discrete fractional calculus.

Keywords: Discrete Prabhakar fractional sum; Discrete fractional difference and sum; Discrete generalized ML functions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005361

DOI: 10.1016/j.chaos.2021.111182

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