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Fractional-like Hukuhara derivatives in the theory of set-valued differential equations

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  • Martynyuk, Anatoliy A.
  • Stamov, Gani Tr.
  • Stamova, Ivanka M.

Abstract

In this paper a fractional-like Hukuhara-type derivative is introduced for a set of equations. Connections between the new defined notion and the classical Hukuhara derivative are established and, in addition, some applications to the theory of set-valued differential equations are discussed. Namely, for a family of equations with fractional-like Hukuhara-type derivatives of the set of states: (a) a version of the comparison principle is proposed; (b) local existence conditions are derived; (c) an estimate of the deviation of the approximate solution from the exact one is given. With this research we extend the theory of fractional-like differential equations to the set-valued case.

Suggested Citation

  • Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304333
    DOI: 10.1016/j.chaos.2019.109487
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    References listed on IDEAS

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    1. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
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    4. Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    5. 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.
    6. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
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    Cited by:

    1. Eghlimi, Hadi & Asgari, Mohammad Sadegh, 2023. "A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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