https://doi.org/10.1140/epjs/s11734-023-00962-x
Regular Article
A time-fractional of a viscoelastic frictionless contact problem with normal compliance
1
Department of Mathematics and Computer Science, Polydisciplinary Faculty, Modeling and Combinatorics Laboratory, Cadi Ayyad University, B.P. 4162, Safi, Morocco
2
Faculty of Science and Technology, Hassan 1st University Settat Laboratory Mathematics, Computer Science and Engineering Sciences (MISI), 26000, Settat, Morocco
3
Department of Mathematics, FPT University, Education zone, Hoa Lac High Tech Park, Km 29 Thang Long Highway, Thach That ward, Hanoi, Vietnam
4
Center for Applied Mathematics of Guangxi, and Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, 537000, Yulin, Guangxi, People’s Republic of China
Received:
15
March
2023
Accepted:
9
August
2023
Published online:
14
September
2023
In this paper, we propose a new model of dynamic frictionless contact problem between a viscoelastic body and a rigid foundation. The constitutive relation is modeled with the fractional Kelvin-Voight law. The contact is described with the normal compliance condition. We derive a weak formulation, and we prove the existence of its weak solution. The proofs are based on the abstract of monotone operator, Caputo derivative, Galerkin method and Banach fixed point theorem.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
