On the new concept of solutions and existence results for impulsive fractional evolution equations

In this paper we discuss the existence of PC-mild solutions for Cauchy problems and nonlocal problems for impulsive fractional evolution equations involving Caputo fractional derivative. By utilizing the theory of operators semigroup, probability density functions via impulsive conditions, a new concept on a PC-mild solution for our problem is introduced. Our main techniques based on fractional calculus and fixed point theorems. Some concrete applications to partial differential equations are considered.