Abstract
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.
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