Solvability and optimal control of semilinear nonlocal fractional evolution inclusion with Clarke subdifferential

Abstract

This article deals with a control system governed by a semilinear nonlocal fractional evolution inclusion with 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 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.

Keywords:

• Solvability
• optimal control
• semilinear fractional evolution inclusion
• Clarke subdifferential
• nonlocal condition

AMS Subject Classifications:

• 34H05
• 34A08
• 49J15

Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471230], [grant number 11671282]. The work of J.C Yao was partially supported by the Grant MOST [106-2923-E-039-001-MY3].