A time-fractional of a viscoelastic frictionless contact problem with normal compliance
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
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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