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

Abstract

In this paper we discuss the existence of P C-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 P C-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. Contents 1. Introduction 345 2. Preliminaries 347 3. New concept of solutions 349 4. Existence results for impulsive Cauchy problems 350 5. Existence results for impulsive nonlocal Cauchy problems 356 6.