Cauchy problem for impulsive fractional differential equations with almost sectorial operators

Abstract

We study a class of non-instantaneous impulsive fractional differential equations in a Banach space. We consider the Cauchy problem with Caputo derivative having variable lower limits and almost sectorial operators. We establish the existence of mild solutions in the space of piecewise continuous functions. We employ the properties of semigroup associated with the almost sectorial operator, theory of measure of non-compactness and fixed point theorems.