Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

2013 ◽  
Vol 11 (3) ◽  
pp. 351-358 ◽  
Author(s):  
P. Muthukumar ◽  
C. Rajivganthi
Keyword(s):  
Differential System ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential System ◽  
Stochastic Functional

Approximate controllability of impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces

2018 ◽  
Vol 36 (2) ◽  
pp. 603-622 ◽  
Author(s):  
Yong Zhou ◽  
S Suganya ◽  
M Mallika Arjunan ◽  
B Ahmad
Keyword(s):  
Differential Equation ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Integro Differential Equation ◽  
State Dependent ◽  
State Dependent Delay ◽  
Non Linear ◽  
Approximately Controllable

Abstract In this paper, the problem of approximate controllability for non-linear impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces is investigated. We study the approximate controllability for non-linear impulsive integro-differential systems under the assumption that the corresponding linear control system is approximately controllable. By utilizing the methods of fractional calculus, semigroup theory, fixed-point theorem coupled with solution operator, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

scholarly journals Approximate controllability of neutral functional differential system with unbounded delay

2001 ◽  
Vol 26 (12) ◽  
pp. 737-744 ◽  
Author(s):  
Jong Yeoul Park ◽  
Sang Nam Kang
Keyword(s):  
Differential Equation ◽  
Control Systems ◽  
Functional Differential Equation ◽  
Differential System ◽  
Approximate Controllability ◽  
Neutral Functional Differential Equation ◽  
Unbounded Delay ◽  
Functional Differential ◽  
Functional Differential System

We consider a class of control systems governed by the neutral functional differential equation with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.

scholarly journals Approximate controllability of impulsive system involving state-dependent delay and variable delay in control via fundamental solution

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2293-2313
Author(s):  
Syed Abdal ◽  
Surendra Kumar
Keyword(s):  
Fundamental Solution ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Variable Delay ◽  
New Class ◽  
State Dependent ◽  
Semilinear Control Systems ◽  
State Dependent Delay

This article is concerned with the approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert spaces. We formulate new sufficient conditions which guarantee the existence of solution to the considered system. We use the theory of fundamental solution, Krasnoselskii?s and Schauder?s fixed point theorems to establish our major results. Finally, two examples are constructed which demonstrate the effectiveness of obtained results.

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