Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

Abstract

We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. Based on a fixed point theorem with regard to condensing map, sufficient conditions for the controllability of the impulsive neutral functional differential inclusions in Banach spaces are derived. Moreover, a remark is given to explain less conservative criteria for special cases, and work is improved in the previous literature.

Existence of Mild Solutions for Hilfer Fractional Neutral Integro-Differential Inclusions via Almost Sectorial Operators

“…The research articles [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] are concerned with the theory of fractional differential systems, and readers will find a number of fascinating findings about fractional dynamical systems. Please refer to [16][17][18][19][20][21] for more information.…”

Approximate Controllability of Fractional Integrodifferential Evolution Equations

“…On the other hand, controllability is an important property of a control system which plays an important role in the analysis and design of control systems [5][6][7][8]. Most literatures in this direction so far have been concerned with controllability of nonlinear differential equations in infinite-dimensional spaces without fractional derivatives (see [9] and references therein). Using generalized open mapping theorem, a set of sufficient conditions for constrained local relative controllability near the origin are formulated and proved for the semilinear systems with delayed controls in [10,11].…”

Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses

“…On the other hand, controllability is the most fundamental concept in modern control theory, which has close connections to pole assignment, structural decomposition, quadratic optimal control, and so forth. Some important results concerning the control theory for various kinds of systems have been obtained in [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and references therein. Kalman et al [19] have investigated the controllability of linear dynamical systems based on the algebraic approach.…”

“…In [25,26], the controllability of the descriptor (singular) systems has been considered. Impulsive control systems with integer derivative have been investigated in [27][28][29]. For integer derivative control systems with state delay and impulses, Zhang et al [27] have derived the sufficient conditions for the controllability based on the fixed point theorem.…”