Coupled time-fractional hemivariational inequalities in frictional thermo-viscoelastic contact problem

Abdelhafid Ouaanabi; Mohammed Alaoui; Mustapha Bouallala; El Hassan Essoufi; Abdelhafid Ouaanabi; Mohammed Alaoui; Mustapha Bouallala; El Hassan Essoufi

doi:10.3934/mmc.2025028

Mathematical Modelling and Control

2025, Volume 5, Issue 4: 400-409. doi: 10.3934/mmc.2025028

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Research article

Coupled time-fractional hemivariational inequalities in frictional thermo-viscoelastic contact problem

1.
University Hassan, Laboratory MSDTE, 26000 Settat, Morocco
2.
Cadi Ayyad University, Polydisciplinary faculty, Modeling and Combinatorics Laboratory, Department of Mathematics and Computer Science B. P. 4162, Safi, Morocco

Received: 01 October 2024 Revised: 02 March 2025 Accepted: 25 March 2025 Published: 04 December 2025

This study examines a quasistatic frictional contact problem involving a thermo-viscoelastic body interacting with a thermally conductive foundation. The constitutive behavior is described by a fractional Kelvin–Voigt model utilizing the Caputo derivative. Heat conduction is modeled through time-fractional displacement and temperature parameters. The contact, friction, and heat exchange are governed by Clarke's subdifferential boundary conditions. The problem is weakly formulated as a system of two coupled time-fractional hemivariational inequalities. The existence of solutions is established by reducing the system to a single time-fractional hemivariational inequality, leveraging recent advances in the theory of time-fractional hemivariational inequalities.
- thermo-viscoelastic materials,
- Caputo derivative,
- frictional contact problem,
- weak solvability,
- Clarke's subdifferential,
- hemivariational inequality
Citation: Abdelhafid Ouaanabi, Mohammed Alaoui, Mustapha Bouallala, El Hassan Essoufi. Coupled time-fractional hemivariational inequalities in frictional thermo-viscoelastic contact problem[J]. Mathematical Modelling and Control, 2025, 5(4): 400-409. doi: 10.3934/mmc.2025028

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Abstract

This study examines a quasistatic frictional contact problem involving a thermo-viscoelastic body interacting with a thermally conductive foundation. The constitutive behavior is described by a fractional Kelvin–Voigt model utilizing the Caputo derivative. Heat conduction is modeled through time-fractional displacement and temperature parameters. The contact, friction, and heat exchange are governed by Clarke's subdifferential boundary conditions. The problem is weakly formulated as a system of two coupled time-fractional hemivariational inequalities. The existence of solutions is established by reducing the system to a single time-fractional hemivariational inequality, leveraging recent advances in the theory of time-fractional hemivariational inequalities.

References

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