Approximate controllability of fractional order non-instantaneous impulsive functional evolution equations with state-dependent delay in Banach spaces. (17th October 2022)

• Record Type: Journal Article
• Authors: Arora, S; Mohan, Manil T; dabas, J
• Is Part Of: IMA journal of mathematical control and information. Volume 39:Number 4(2022)
• Page Start: 1103
• Page End: 1142
• Publication Date: 2022-10-17
• Subjects: approximate controllability -- non-instantaneous impulses -- state-dependent delay -- fractional differential equation -- fixed point theorem. Mathematics Subject Classication (2020): 34K06, 34A12, 37L05, 93B05; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnac024
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: This paper deals with the control problems governed by fractional impulsive functional evolution equations with state-dependent delay involving Caputo fractional derivatives in Banach spaces. The main objective of this work is to formulate sufficient conditions for the approximate controllability of the considered system in separable reflexive Banach spaces. We have exploited the resolvent operator technique and Schauder's fixed point theorem in the proofs to achieve this goal. The approximate controllability of linear system is discussed in detail, which lacks in the existing literature. Moreover, we point out some shortcomings of the existing works in the context of characterization of mild solution, phase space, and approximate controllability of fractional order impulsive systems in Banach spaces. Finally, we investigate the approximate controllability of the fractional order heat equation with non-instantaneous impulses and delay by using the developed results.