Coupled system of fractional hemivariational inequalities with applications

ABSTRACT

The aim of the paper is to study a coupled system which consists of a fractional differential hemivariational inequality (FDHVI, for short) combined with a fractional hemivariational inequality (FHVI, for short). By utilizing Rothe method and surjectivity result, the existence of coupled system is established. In addition, we apply the results to a new quasistatic contact problem, in which the constitutive equations are described by the fractional Kelvin-Voigt laws.

KEYWORDS:

• Coupled system
• Rothe method
• existence
• contact problem

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 26A33
• 74F99

Acknowledgments

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 12161015], Guizhou Data Driven Modeling Learning and Optimization Innovation Team [grant number [2020]5016], Super Computing Algorithm and Application Laboratory of Guizhou University and Gui'an Scientific Innovation Company [grant number K22-0116-003], and Guangxi Natural Science Foundation [grant number 2021GXNSFAA075022].