Controllability of second-order impulsive neutral functional differential inclusions in Banach spaces

Abstract

In this paper, we shall prove the controllability of second-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi-valued mappings. As an example, we also consider an second-order impulsive neutral functional differential equation with infinite delay.

Relative controllability of nonlinear neutral fractional integro‐differential systems with distributed delays in control

“…Hence, the hypotheses of Theorem 3.3 are satisfied, and the nonlinear system (20) is controllable on J.…”

“…It is motivating to introduce fractional derivative for these models and study their qualitative behaviors.Controllability is one of the most important qualitative behaviors of dynamical systems. Controllability of nonlinear integer order systems in both finite and infinite dimensional spaces has been extensively studied [19,20]. Fractional control theory is a generalization of the classical control theory.…”

Controllability of Second-Order Impulsive Functional Differential Equations With State-Dependent Delay

“…The concept of controllability plays an important role in the analysis and design of control systems. Controllability of nonlinear systems with and without impulses has been studied by many authors [3,22,[26][27][28]30]. For more details on impulsive differential equations and on their applications, we refer to the monographs of Lakshmikantham et al [24] and Samoilenko and Perestyuk [31] and the references therein.…”

Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

“…Ahmed [10] first introduced three different models of impulsive differential inclusions and studied the existence of them, respectively. From then on, there have been many focuses on various properties of impulsive differential inclusions, see [11][12][13][14][15][16][17] and references therein.…”

“…Controllability is one of the primary problems in control theory [11,13,14,[17][18][19][20][21][22][23][24]. Study on controllability has always been considered as a hot topic given its numerous applications to mechanics, electrical engineering, medicine, biology, and so forth.…”