On the mild solution for nonlocal impulsive fractional semilinear differential inclusion in Banach spaces

Document Type : Research Article


Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004(MS), India


This paper gives existence results for impulsive fractional semilinear differential inclusions involving Caputo derivative in Banach spaces. We are concerned with the case when the linear part generates a semigroup not necessarily compact, and the multivalued function is upper semicontinuous and compact. The methods used throughout the paper range over applications of Hausdorff measure of noncompactness, and multivalued fixed point theorems. Finally, we provide an example to clarify our results.