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

Author:

CENG LU-CHUAN1ORCID,CHEN BOLING2ORCID,LIAO SHANLI2ORCID,NGUYEN VAN THIEN3ORCID,YAO JEN-CHIH45ORCID

Affiliation:

1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

2. 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

3. Department of Mathematics, FPT University, Education zone, Hoa Lac High Tech Park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam

4. Center for General Education, China Medical University, Taichung, Taiwan, ROC

5. 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.

Funder

Natural Science Foundation of Guangxi

Research Ability Enhancement Project of Young and Middle-Aged Teachers in Guangxi Colleges and University

2020 Shanghai Leading Talents Program of the Shanghai Municipal Human Resources and Social Security Bureau

Innovation Program of Shanghai Municipal Education Commission

Program for Outstanding Academic Leaders in Shanghai City

MOST

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

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