SOLVABILITY AND OPTIMAL CONTROL OF A SYSTEM OF SEMILINEAR NONLOCAL FRACTIONAL EVOLUTION INCLUSIONS WITH PARTIAL CLARKE SUBDIFFERENTIAL

Lu-Chuan Ceng (), Boling Chen, Shanli Liao (), Nguyen van Thien () and Jen-Chih Yao ()
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China
Boling Chen: Center for Applied Mathematics of Guangxi and Guangxi Colleges and Universities Key Laboratory of Complex, System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, P. R. China
Shanli Liao: Center for Applied Mathematics of Guangxi and Guangxi Colleges and Universities Key Laboratory of Complex, System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, P. R. China
Nguyen van Thien: Department of Mathematics, FPT University, Education zone, Hoa Lac High Tech Park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam
Jen-Chih Yao: Center for General Education, China Medical University, Taichung, Taiwan, ROC, Academy of Romanian Scientists, 50044, Bucharest, Romania

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-20

Abstract: The purpose of this paper is to deal with a system governed by a system of semilinear nonlocal fractional evolution inclusions with partial Clarke subdifferential and its optimal control. First, we establish an existence theorem of the mild solution for the presented control system by applying the measure of noncompactness, a fixed point theorem of a condensing multivalued map and some properties of partial Clarke subdifferential. Moreover, under some mild conditions, we obtain a result on the existence of an optimal control to the presented control system. Finally, an example is provided to demonstrate the main results. The results presented in this paper improve, extend and develop the corresponding results in the earlier and recent literature.

Keywords: Solvability; Optimal Control; System of Semilinear Fractional Evolution Inclusions; Partial Clarke Subdifferential; Nonlocal Condition (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400097

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