Approximate controllability for fractional semilinear parabolic equations. (1st June 2019)

• Record Type: Journal Article
• Authors: Huang, Yong; Liu, Zhenhai; Wen, Ching-Feng
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 11(2019)
• Page Start: 2971
• Page End: 2979
• Publication Date: 2019-06-01
• Subjects: Fractional parabolic systems -- Approximate controllability -- Semigroup theory -- Mild solution -- Fixed point theorem; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.08.003
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we deal with the control systems described by a large class of fractional semilinear parabolic equations. Firstly, we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate Banach space. Secondly, we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator, nonlinear analysis method and fixed point theorem. Then, the approximate controllability of the fractional semilinear parabolic equations is formulated and proved. At the end of the paper, an example is given to illustrate our main results.