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On Hilfer Generalized Proportional Nabla Fractional Difference Operators

Author

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  • Qiushuang Wang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Run Xu

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, the Hilfer type generalized proportional nabla fractional differences are defined. A few important properties in the left case are derived and the properties in the right case are proved by Q -operator. The discrete Laplace transform in the sense of the left Hilfer generalized proportional fractional difference is explored. Furthermore, An initial value problem with the new operator and its generalized solution are considered.

Suggested Citation

  • Qiushuang Wang & Run Xu, 2022. "On Hilfer Generalized Proportional Nabla Fractional Difference Operators," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2654-:d:874412
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    References listed on IDEAS

    as
    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. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
    3. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
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