Controllability of nonlocal neutral impulsive differential equations with measure of noncompactness

Chalishajar, Dimplekumar; Karthikeyan, K.; Tamizharasan, Dhatchinamoorthy

doi:10.12988/ijma.2021.912199

Cited by 3 publications

(1 citation statement)

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“…Next, we investigated the existence and uniqueness of the controllability of neutral impulsive differential equations with nonlocal conditions in prior work. The controllability of a nonlocal neutral impulsive differential equation under compactness conditions, Lipschitz conditions, and mixed-type conditions is obtained using the property of measure of noncompactness and Darbo-Sadovskii's fixed point theorem, read the cited papers [38,39]. We now extend our research to investigate the controllability and wellposedness of an impulsive functional abstract second order differential equation with state dependent delay.…”

Section: Introductionmentioning

confidence: 85%

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

Karthikeyan

Tamizharasan²,

Chalishajar

2021

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The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation.

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Section: Introductionmentioning

confidence: 85%

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

Karthikeyan

Tamizharasan²,

Chalishajar

2021

Axioms

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Nonlocal integro-differential equations of Sobolev type in Banach spaces involving $$\psi$$-Caputo fractional derivative

Liang

Xiao

2021

Banach J. Math. Anal.

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Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative

Rabhi

Horani

2022

MATH

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<abstract><p>In this paper, we investigate the existence of mild solutions for nonlocal delay fractional Cauchy problem with Caputo conformable derivative in Banach spaces. We establish a representation of a mild solution using a fractional Laplace transform. The existence of such solutions is proved under certain conditions, using the Mönch fixed point theorem and a general version of Gronwall's inequality under weaker conditions in the sense of Kuratowski measure of non compactness. Applications illustrating our main abstract results and showing the applicability of the presented theory are also given.</p></abstract>

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Controllability of nonlocal neutral impulsive differential equations with measure of noncompactness

Cited by 3 publications

References 0 publications

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

Nonlocal integro-differential equations of Sobolev type in Banach spaces involving $$\psi$$-Caputo fractional derivative

Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative

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