Controllability of Neutral Impulsive Differential Inclusions with Non-Local Conditions

Anguraj

Karthikeyan³

et al. 2016

Preprint

Section: S Acharya Studied Controllability Of Neutral Impulsive Diffmentioning

confidence: 99%

A study of controllability of impulsive neutral evolution integro-differential equations with state dependent delay in Banach space

Anguraj

Karthikeyan³

et al. 2016

Preprint

“…Nowadays, researchers are engaged to overcome this problem, refer to [4,9]. Very recently, Chalishajar et al [10][11][12] studied the controllability of second order neutral functional differential inclusion, with infinite delay and impulse effect on unbounded domain, without compactness of the family of cosine operators. Ntouyas and O'Regan [13] made some remarks on controllability of evolution equations in Banach paces and proved a result without compactness assumption.…”

Section: Introductionmentioning

confidence: 99%

Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay

2012

J Optim Theory Appl

Self Cite

This paper is concerned with controllability of a partial neutral functional differential inclusion of second order with impulse effect and infinite delay. We introduce a new phase space to prove the controllability of an inclusion which consists of an impulse effect with infinite delay. We claim that the phase space considered by different authors is not correct. We establish the controllability of mild solutions using a fixed point theorem for contraction multi-valued maps and without assuming compactness of the family of cosine operators.Keywords Controllability · Second order impulsive neutral differential inclusions · Fixed point theorem for multi-valued maps · Strongly continuous cosine family

“…is a Caputo fractional partial derivative of order q ∈ (0, 1). To write the system (35)- (38) to the form {(1),(2),(3)}, we take…”

mentioning

confidence: 99%

Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

Ravichandran²,

Dhanalakshmi³

et al. 2019

ASI

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.