Approximate Controllability of a Fractional Neutral Differential System with Deviated Argument in a Banach Space

详细信息    查看全文

• 作者：Sanjukta Das ; Dwijendra N. Pandey…
• 关键词：Approximate controllability ; Deviated argument ; Fractional neutral differential equation
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：25
• 期：1
• 页码：65-82
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Engineering, general; Computer Science, general;
• 出版者：Springer India
• ISSN：0974-6870
• 卷排序：25

文摘

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.