Controllability of Non-densely Defined Neutral Functional Differential Systems in Abstract Space*

Abstract

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.

Controllability of Non-Densely Defined Abstract Mixed Volterra–fredholm Neutral Functional Integrodifferential Equations

“…The aim of the present paper is to investigate the controllability for the non-densely defined system (1.1)-(1.2) by using Sadovskii fixed point theorem. The results obtained in this paper generalizes the results of [11,12] and also can be regarded as a continuation and an extension of those for densely defined control systems.…”

“…Fu [11] studied the controllability result for non-densely defined functional differential systems, Fu and Liu [12] extended the problem to neutral systems, Benchohra et al [6] established controllability results for non-densely defined semilinear functional differential equations, Li [21] established sufficient conditions ensuring the existence of integral solutions and strict solutions of non-densely defined impulsive functional differential equations. Kavitha and Mallika Arjun [15] studied controllability results for non-densely defined impulsive functional differential equations with infinite delay in Banach spaces.…”

Controllability Problem of Fractional Neutral Systems: A Survey

“…A standard approach is to transform the controllability problem into a fixed point problem for an appropriate operator in a functional space. There are many papers devoted to the controllability problem, in which authors used the theory of fractional calculus [3][4][5][6][7][8][9][10][11][12][13] and a fixed point approach [14][15][16][17][18][19][20][21][22][23].…”

Controllability of non-densely defined impulsive neutral functional differential systems with infinite delay in Banach spaces

“…In recent years, the problem of controllability for various kinds of differential and impulsive differential systems has been extensively studied by many authors [11][12][13][14][15][16][17]9,18] using different approaches. Recently, Chang et al [4] studied the controllability of impulsive neutral functional differential systems with infinite delay in Banach spaces by using Dhage's fixed point theorem.…”