On some impulsive fractional neutral differential systems with nonlocal condition through fractional operators

Abstract

According to semigroup theories, fractional calculus, Banach contraction principle and Sadovskii fixed point theorem, this paper is fundamentally involved with  the existence of mild solutions for an impulsive fractional neutral differential systems (abbreviated, IFNDS) with nonlocal conditions (abbreviated, NLC) in Banach space $\x$.  At last, an illustration is also presented to exhibit the use of our theoretical results.