Approximate controllability for fractional semilinear parabolic equations |
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| Authors: | Yong Huang Zhenhai Liu Ching-Feng Wen |
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| Affiliation: | 1. Department of Mathematics, Baise University, Baise 533000, Guangxi Province, PR China;2. Guangxi Universities Key Laboratory of Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, PR China;3. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan;4. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan |
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| 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. |
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| Keywords: | Fractional parabolic systems Approximate controllability Semigroup theory Mild solution Fixed point theorem |
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