Existence and controllability results of impulsive fractional neutral integro-differential equation with sectorial operator and infinite delay

Chalishajar, Dimplekumar; Malar, K.; Ilavarasi, R.

doi:10.1063/1.5127471

Cited by 9 publications

(9 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Many basic problems of Control Theory like pole-assignment, structural engineering, and optimal control, may be solved under the assumption that the linear system is controllable. In recent years, significant progress has been made in the controllability of linear and nonlinear deterministic systems [1,9,10,12,16,30].…”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlocal impulsive functional differential equations with measure of noncompactness in Banach spaces

Chalishajar¹,

Karthikeyan²,

Tamizharasan³

2021

J. Nonlinear Sci. Appl.

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii's fixed point theorem, we get the controllability of nonlocal impulsive differential equations under compactness conditions, Lipschitz conditions, and mixed-type conditions, respectively.

show abstract

Section: Introductionmentioning

confidence: 99%

Controllability of nonlocal impulsive functional differential equations with measure of noncompactness in Banach spaces

Chalishajar¹,

Karthikeyan²,

Tamizharasan³

2021

J. Nonlinear Sci. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…ere are many practical examples of impulsive control systems which are modeled by impulsive differential equations (for more information, see the monographs: Samoilenko and Perestyuk [6]; Franco and Nieto [7]; Sun and Zhang [8]; Lakshmikanthan, Bainov and Simeonov [9]; He and Yu [10]; Luo and Shen [11]). e controllability of impulsive evolution equations has been studied recently for several authors, but most them study the exact controllability only (to mention, Radhakrishnan and Balachandran [12]; Chalishajar [13]; Selvi and Mallika [14]). To our knowledge, there are a few works on approximate controllability of impulsive semilinear evolution equations (to mention, Chen and Li [15] and Sakthivel and Anandhi [16]).…”

Section: Introductionmentioning

confidence: 99%

Controllability of Impulsive Semilinear Stochastic Heat Equation with Delay

Leiva

Narvaez

Sivoli

2020

International Journal of Differential Equations

View full text Add to dashboard Cite

LaSalle wrote the following: “it is never possible to start the system exactly in its equilibrium state, and the system is always subject to outside forces not taken into account by the differential equations. The system is disturbed and is displaced slightly from its equilibrium state. What happens? Does it remain near the equilibrium state? This is stability. Does it remain near the equilibrium state and in addition tend to return to the equilibrium? This is asymptotic stability.” Continuing with what LaSalle said, we conjecture that real-life systems are always under the influence of impulses, delays, memory, nonlocal conditions, and noises, which are intrinsic phenomena no taken into account by the mathematical model that is representing by a differential equation. For many control systems in real life, delays, impulses, and noises are natural properties that do not change their behavior. So, we conjecture that, under certain conditions, the abrupt changes, delays, and noises as perturbations of a system do not modify certain properties such as controllability. In this regard, we prove the interior S ∗ -controllability of the semilinear stochastic heat equation with impulses and delay on the state variable, and this is done by using new techniques avoiding fixed point theorems employed by Bashirov et al.

show abstract

“…The controllability of impulsive evolution equations has been studied recently for several authors, but most of them study the exact controllability only, for example: Chalishajar [], studied the exact controllability of impulsive partial neutral functional differential equations with infinite delay, Radhakrishnan and Balachandran [] studied the exact controllability of semilinear impulsive integrodifferential evolution systems with nonlocal conditions and Selvi and Arjunan [] studied the exact controllability for impulsive differential systems with finite delay.…”

Section: Introductionmentioning

confidence: 99%

Impulsive semilinear heat equation with delay in control and in state

Camacho

Leiva

2019

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable.After that, we add impulses and a nonlinear perturbation with delay in state, and using Rothe's fixed point theorem, we prove that the interior approximate controllability of the impulsive semilinear system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear diffusion process in Hilbert spaces with delay in control and in state.

show abstract

Existence and controllability results of impulsive fractional neutral integro-differential equation with sectorial operator and infinite delay

Cited by 9 publications

References 32 publications

Controllability of nonlocal impulsive functional differential equations with measure of noncompactness in Banach spaces

Controllability of nonlocal impulsive functional differential equations with measure of noncompactness in Banach spaces

Controllability of Impulsive Semilinear Stochastic Heat Equation with Delay

Impulsive semilinear heat equation with delay in control and in state

Contact Info

Product

Resources

About