Approximate controllability of fractional delay evolution inclusions with noncompact semigroups

ABSTRACT

This paper is devoted to investigate the control systems governed by nonlinear fractional delay evolution inclusions (FDEIs) with noncompact semigroups. Under suitable assumptions, sufficient conditions for approximate controllability of FDEIs are established. The approximate controllability results are further extended to FDEIs with nonlocal conditions, where the compactness or Lipschitz continuity on the nonlocal functions is not required. Finally, two examples are given to illustrate the effectiveness of our conclusions.

Keywords:

• Approximate controllability
• fractional evolution inclusion
• delay
• nonlocal condition

AMS Subject Classifications:

• Primary 35R11
• Secondary 34K09
• 34K35

Acknowledgements

The authors would like to thank reviewers for their insightful and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Foundation for Distinguished Young Talents in Higher Education of Guangdong, China [grant no. 2018KQNCX307].