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

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

Chaos, Solitons & Fractals, 2020, vol. 131, issue C

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.

Keywords: Fractional-like derivative; Hukuhara differentiable; Set-valued differential equations; Local existence; Comparison result (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304333

DOI: 10.1016/j.chaos.2019.109487

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