Local and Global Existence of Mild Solution to Fractional Semilinear Impulsive Volterra Type Integro-Differential Equation

This paper is concerned with the local and global existence of mild solution for an impulsive fractional semilinear Volterra type integro differential equation with noncompact semigroup in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, examples are given to illustrate that our results are valuable.