Controllability of impulsive differential systems with nonlocal conditions

Monotone iterative method for abstract impulsive integro-differential equations with nonlocal conditions in Banach spaces

“…In 2009, Liang et al [32] combined the impulsive conditions and the nonlocal conditions, and investigated the nonlocal problem of impulsive evolution equations in Banach spaces. Later on, Fan [19], Fan and Li [20], Ji et al [26] studied the impulsive evolution equations with nonlocal conditions. In previous works, nonlocal problems have been studied by many authors using different tools, such as Banach contraction mapping principal, Schauder's fixed-point theorem, Sadovskii's fixed-point theorem and Mönch fixed-point theorem.…”

“…There has been a significant development in impulsive evolution equations in Banach spaces. For more details on this theory and its applications, we refer to the references [1], [2], [10], [11], [19], [20], [26], [32], [35], [38].…”

Exact Controllability for Hilfer Fractional Differential Inclusions Involving Nonlocal Initial Conditions

“…Controllability is one of the fundamental concepts in mathematical control theory, it means that it is possible to steer a dynamical system from an arbitrary initial state to arbitrary final state using the set of admissible controls. Recently, the controllability conditions for various linear and nonlinear integer or fractional order systems have been considered in many papers by using different methods [20][21][22][23][24][25][26][27][28][29][30][31][32][33] and the references. There have also been some results [20-24, 32, 33] about the investigations of the exact controllability of systems represented by nonlinear evolution equations in infinite dimensional space.…”

Controllability results for impulsive differential systems with finite delay

“…The concept of controllability plays an important role in many areas of applied mathematics. In recent years, significant progress has been made in the controllability of linear and nonlinear deterministic systems [6,11,17,19]. In [11], the author studied the controllability of impulsive functional differential systems of the form x (t) = A(t)x(t) + f (t, x(t)) + (Bu)(t), a.e.…”

“…In [11], the author studied the controllability of impulsive functional differential systems of the form x (t) = A(t)x(t) + f (t, x(t)) + (Bu)(t), a.e. on [ Motivated by the above mentioned works [7,11,15,23], the main purpose of this paper is to establish the sufficient conditions for the controllability of impulsive differential system with finite delay of the form x (t) = A(t)x(t) + f (t, x t ) + (Bu)(t), (1.1)…”