History-dependent generalized fractional differential hemivariational inequalities with application to contact mechanics

Furi Guo; Furi Guo

doi:10.3934/math.2026053

AIMS Mathematics

2026, Volume 11, Issue 1: 1239-1265. doi: 10.3934/math.2026053

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Research article

History-dependent generalized fractional differential hemivariational inequalities with application to contact mechanics

Furi Guo ^,

School of Mathematics and statistics Shanxi Datong University, Datong 037009, Shanxi, China

Received: 13 November 2025 Revised: 19 December 2025 Accepted: 24 December 2025 Published: 16 January 2026
MSC : 47J22, 49J40, 74M10, 74M15

In this paper, we investigate a class of $ \psi $-Caputo fractional differential hemivariational inequalities with history-dependent operators. By employing the Rothe method in conjunction with surjectivity results for multivalued pseudomonotone operators, the solvability of weak solutions to $ \psi $-Caputo fractional differential hemivariational inequalities is obtained. As an application, a class of history-dependent viscoelastic friction contact problems that account for adhesion phenomena is investigated. In this contact model, the friction and contact conditions are described by Clarke generalized gradient of two nonconvex and nonsmooth function involving adhesion. Finally, the solvability of the solution for this friction contact model is established.
- hemivariational inequality,
- history-dependent operator,
- adhesion,
- $ \psi $-Caputo fractional derivatives,
- viscoelastic contact model
Citation: Furi Guo. History-dependent generalized fractional differential hemivariational inequalities with application to contact mechanics[J]. AIMS Mathematics, 2026, 11(1): 1239-1265. doi: 10.3934/math.2026053

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Abstract

In this paper, we investigate a class of $ \psi $-Caputo fractional differential hemivariational inequalities with history-dependent operators. By employing the Rothe method in conjunction with surjectivity results for multivalued pseudomonotone operators, the solvability of weak solutions to $ \psi $-Caputo fractional differential hemivariational inequalities is obtained. As an application, a class of history-dependent viscoelastic friction contact problems that account for adhesion phenomena is investigated. In this contact model, the friction and contact conditions are described by Clarke generalized gradient of two nonconvex and nonsmooth function involving adhesion. Finally, the solvability of the solution for this friction contact model is established.

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