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Solvability And Optimal Control Of A System Of Semilinear Nonlocal Fractional Evolution Inclusions With Partial Clarke Subdifferential

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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)

  • VAN THIEN NGUYEN

    (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)

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.

Suggested Citation

  • Lu-Chuan Ceng & Boling Chen & Shanli Liao & Van Thien Nguyen & Jen-Chih Yao, 2024. "Solvability And Optimal Control Of A System Of Semilinear Nonlocal Fractional Evolution Inclusions With Partial Clarke Subdifferential," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-20.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400097
    DOI: 10.1142/S0218348X24400097
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