An analysis on approximate controllability results for impulsive fractional differential equations of order 1 < r < 2 with infinite delay using sequence method

Abstract

In this work, we discuss the existence and approximate controllability results for impulsive fractional differential systems of order with infinite delay. Sectorial operator of type , the nonlinear alternative of the Leray–Schauder fixed point theorem, sequence method, and impulsive systems have been used to establish these results. First, we investigate the existence of mild solutions for impulsive fractional differential equations of order . We also establish the approximate controllability results for the nonlocal fractional delay differential equations. An example is also given to illustrate our main results.