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The Cauchy problem of fuzzy differential equations under generalized differentiability. (English) Zbl 1263.34007
Authors’ abstract: The generalization of the concept of H-differentiability may be of great help in the dynamic study of fuzzy differential equations. In this paper, the concept of generalized differentiability is described from a new perspective. On the basis of this concept, the class of differentiable fuzzy set-valued mappings is enlarged. The Cauchy problem for fuzzy differential equations is investigated in this enlarged setting. As a result, some new solutions are obtained. The lengths of the support sets of these solutions may be non-monotonic. Several examples are also presented.

##### MSC:
 34A07 Fuzzy ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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