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Discrete Prabhakar fractional difference and sum operators

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  • Mohammed, Pshtiwan Othman
  • Abdeljawad, Thabet
  • Hamasalh, Faraidun Kadir

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.

Suggested Citation

  • Mohammed, Pshtiwan Othman & Abdeljawad, Thabet & Hamasalh, Faraidun Kadir, 2021. "Discrete Prabhakar fractional difference and sum operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005361
    DOI: 10.1016/j.chaos.2021.111182
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    References listed on IDEAS

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    1. Pshtiwan Othman Mohammed, 2019. "A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(4), pages 43-50, August.
    2. Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    3. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    4. Abdeljawad, Thabet, 2018. "Different type kernel h−fractional differences and their fractional h−sums," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 146-156.
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