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Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators

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  • Mohammed, Pshtiwan Othman
  • Kürt, Cemaliye
  • Abdeljawad, Thabet

Abstract

Based on the recently published article about bivariate Mittag-Leffler function Eα,β,γδ(x) by Fernandez et al. (2020), we introduce the bivariate discrete Mittag-Leffler function, denoted by Eα,β,γ¯δ(λ1,λ2;x), as a discrete version of the results of Fernandez et al. under some constraints in this study. We establish this new definition to find a fractional difference equation. Then, we employ the fractional sum and differences formulas to get the results with respect to the bivariate discrete Mittag-Leffler function. Moreover, we give the discrete Laplace transform of the corresponding discrete function and build up the discrete sum operator to show up the semigroup property on some constraints. Also, left inverse of the discrete sum operator is given. Finally, we end the paper by two examples and conclusion.

Suggested Citation

  • Mohammed, Pshtiwan Othman & Kürt, Cemaliye & Abdeljawad, Thabet, 2022. "Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s096007792201027x
    DOI: 10.1016/j.chaos.2022.112848
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Abdeljawad, Thabet, 2018. "Different type kernel h−fractional differences and their fractional h−sums," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 146-156.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
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    Cited by:

    1. Zeng, Junwei & Qian, Yongsheng & Wang, Wenhai & Xu, Dejie & Li, Haijun, 2023. "The impact of connected automated vehicles and platoons on the traffic safety and stability in complex heterogeneous traffic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    2. Almusawa, Musawa Yahya & Mohammed, Pshtiwan Othman, 2023. "Approximation of sequential fractional systems of Liouville–Caputo type by discrete delta difference operators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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