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Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences

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  • Suwan, Iyad
  • Abdeljawad, Thabet
  • Jarad, Fahd

Abstract

In this article, benefiting from the nabla h−fractional functions and nabla h−Taylor polynomials, some properties of the nabla h−discrete version of Mittag-Leffler (h−ML) function are studied. The monotonicity of the nabla h−fractional difference operator with h−ML kernel (Atangana–Baleanu fractional differences) is discussed. As an application, the Mean Value Theorem (MVT) on hZ is proved.

Suggested Citation

  • Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:50-59
    DOI: 10.1016/j.chaos.2018.10.010
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    References listed on IDEAS

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    1. 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.
    2. Fahd Jarad & Thabet Abdeljawad & Dumitru Baleanu & Kübra Biçen, 2012. "On the Stability of Some Discrete Fractional Nonautonomous Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, February.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    5. S. J. Sadati & D. Baleanu & A. Ranjbar & R. Ghaderi & T. Abdeljawad (Maraaba), 2010. "Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-7, August.
    6. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
    7. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    8. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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    Cited by:

    1. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    2. Panda, Sumati Kumari & Abdeljawad, Thabet & Ravichandran, C., 2020. "A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Rashid, Saima & Sultana, Sobia & Hammouch, Zakia & Jarad, Fahd & Hamed, Y.S., 2021. "Novel aspects of discrete dynamical type inequalities within fractional operators having generalized ℏ-discrete Mittag-Leffler kernels and application," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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