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On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels

Author

Listed:
  • Thabet Abdeljawad

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

  • Arran Fernandez

    (Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, Cambridge CB3 0WA, UK
    Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99628 Famagusta, North Cyprus, via Mersin 10, Turkey)

Abstract

We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

Suggested Citation

  • Thabet Abdeljawad & Arran Fernandez, 2019. "On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:772-:d:260059
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    References listed on IDEAS

    as
    1. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    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.
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