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Peer-reviewedCC BY 4.0Fractal and Fractional

Solvability of a New Class of ψ-Fractional Unilateral Constrained Friction Problems

  • Furi Guo1
  • Fang Luo1
  • Shugui Kang1
  1. 1School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
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Abstract

A new type of frictional contact problem is proposed in this paper. The nonlinear viscoelastic constitutive relationship we are considering contains ψ-fractional differential terms. The contact conditions are controlled by fractional unilateral constraint conditions. The friction condition is given by a the generalized Clarke multivalued subdifferential function. Initially, by integrating Green’s theorem with findings from the multivalued operator theory, the problem is rephrased into a variational–hemivariational inequality framework. Subsequently, semi-discretization techniques are employed to establish the solvability of variational–hemivariational inequalities. Ultimately, these theoretical outcomes are transplanted to the friction contact model scenario, thus proving the existence of the latter’s solution.

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Cite

BibTeXRIS
BibTeX
@article{guo2026solvability,
  title = {{Solvability of a New Class of ψ-Fractional Unilateral Constrained Friction Problems}},
  author = {Furi Guo and Fang Luo and Shugui Kang},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10100694},
  url = {https://www.mdpi.com/2504-3110/10/10/694},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Solvability of a New Class of ψ-Fractional Unilateral Constrained Friction Problems
AU  - Furi Guo
AU  - Fang Luo
AU  - Shugui Kang
PY  - 2026
DA  - 2026/10/03
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10100694
UR  - https://www.mdpi.com/2504-3110/10/10/694
AB  - A new type of frictional contact problem is proposed in this paper. The nonlinear viscoelastic constitutive relationship we are considering contains ψ-fractional differential terms. The contact conditions are controlled by fractional unilateral constraint conditions. The friction condition is given by a the generalized Clarke multivalued subdifferential function. Initially, by integrating Green’s theorem with findings from the multivalued operator theory, the problem is rephrased into a variational–hemivariational inequality framework. Subsequently, semi-discretization techniques are employed to establish the solvability of variational–hemivariational inequalities. Ultimately, these theoretical outcomes are transplanted to the friction contact model scenario, thus proving the existence of the latter’s solution.
SN  - 2504-3110
ER  -