The purpose of this study is to look at a family of starting value problem for semilinear fuzzy fractional elliptic equation with fractional Caputo derivatives. Firstly, we are going to extend the definition of laplacian operator under generalized H-differentiability in the Fuzzy systems. Secondly, the fuzzy integral equation are founded. Then, the existence and uniqueness of a fuzzy solution are etablished utilizing the Banach fixed point assessment method under Lipschitz conditions. Finally, we conclude our work by a conclusion.

The aim of this work is to study the existence of solutions for nonlocal fractional differential equations inclusions involving ?-Caputo fractional dirivative in Banach space. The proofs are based on the noncompactness measure method. As application, we give an example is given to illustrate the theoretical results.