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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9961
Title: Approximate Controllability of a Fractional Neutral Differential System with Deviated Argument in a Banach Space
Authors: Das S.
Pandey D.N.
Sukavanam N.
Published in: Differential Equations and Dynamical Systems
Abstract: In this paper, a fractional order neutral differential equation with deviated argument is studied. The existence and uniqueness of mild solution are obtained by using Banach contraction principle without imposing additional assumptions such as compactness, analyticity, uniform boundedness etc. We also discuss the approximate controllability of a fractional neutral differential equation with deviated argument by assuming a simple range condition (HR). Thereby, we remove the need to assume the invertibility of a controllability operator used by Tai (Appl. Math. Lett. 24: 2158–2161, 2011), which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by Sakthivel et al. (Rep. Math. Phys. 70: 291–311, 2012), which are practically difficult to verify and apply. An example is provided to illustrate the presented theory. © 2015, Foundation for Scientific Research and Technological Innovation.
Citation: Differential Equations and Dynamical Systems (2017), 25(1): 65-82
URI: https://doi.org/10.1007/s12591-015-0237-y
http://repository.iitr.ac.in/handle/123456789/9961
Issue Date: 2017
Publisher: Springer (India) Private Ltd.
Keywords: Approximate controllability
Deviated argument
Fractional neutral differential equation
ISSN: 9713514
Author Scopus IDs: 56303959200
7103025354
12804420600
Author Affiliations: Das, S., Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, India
Pandey, D.N., Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, India
Sukavanam, N., Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, India
Corresponding Author: Das, S.; Department of Mathematics, IIT RoorkeeIndia; email: sanjukta_das44@yahoo.com
Appears in Collections:Journal Publications [MA]

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