Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces

This paper introduces a new concept called impulsive control inclusion condition, i.e., the impulsive condition is presented, in the first time, as inclusion related to multivalued maps and controls. The notion of approximate controllability of a class of semilinear Hilfer fractional differential control inclusions in Banach spaces is established. For the main results, we use fractional calculus, fixed point technique, semigroup theory and multivalued analysis. An appropriate set of sufficient conditions for the considered system to be approximately controllable is studied. Finally, we give an illustrated example to provide the obtained theory.