Sobolev type fractional delay impulsive equations with Alpha-Sobolev resolvent families and integral conditions

Abstract

We introduce a new tool called alpha-Sobolev resolvent family to establish the existence and uniqueness of solutions for a class of some fractional delay quasilinear integro-differential equations with nonlocal and impulsive conditions of Sobolev type. We use fractional calculus, resolvent family and Banach fixed point theorem for the main result. Further, we give a provided example to illustrate the abstract results.