Approximate controllability of impulsive Hilfer fractional differential inclusions

In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new PC1−ν-mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory. 0c 2017 All rights reserved.