The Cauchy problem of fuzzy differential equations under generalized differentiability

The generalization of the concept of H-differentiability can 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 shown.