Differentiability of multivalued functions on time scales and applications to multivalued dynamic equations

In this paper, a class of new derivatives of multivalued functions on a time scale, called the Hukuhara–Hilger derivative, suited to our study of multivalued dynamic equations is developed. Moreover, some corresponding properties of the Hukuhara–Hilger derivative are discussed. The proposed approach forms the appropriate environment within which the study of multivalued dynamic inclusions on time scales can be developed. A first example of multivalued dynamic equations is included.