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On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations

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  • Kucche, Kishor D.
  • Mali, Ashwini D.
  • Fernandez, Arran
  • Fahad, Hafiz Muhammad

Abstract

We investigate the Hilfer-type operator within the topic of tempered fractional calculus with respect to functions. This operator, the tempered Ψ-Hilfer derivative, is defined for the first time here, and its fundamental properties are studied, such as composition properties, function space mappings, and other functional analysis properties. We also consider fractional differential equations involving these operators, and establish existence, uniqueness, well-posedness, and stability results for such equations under suitable conditions.

Suggested Citation

  • Kucche, Kishor D. & Mali, Ashwini D. & Fernandez, Arran & Fahad, Hafiz Muhammad, 2022. "On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s096007792200741x
    DOI: 10.1016/j.chaos.2022.112547
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    References listed on IDEAS

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    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Jingwei Deng & Weiyuan Ma & Kaiying Deng & Yingxing Li, 2020. "Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
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    1. Luís P. Castro & Anabela S. Silva, 2023. "On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems," Mathematics, MDPI, vol. 11(2), pages 1-22, January.

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