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This research aims to analyze a mathematical model of contact between a deformable body and an obstacle, incorporating time-fractional derivatives.

June 10, 2026FractalsOpen Access

A Penalization Method for a Time-Fractional Differential Contact Problem with Unilateral Constraints and Coulomb Friction

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This research aims to analyze a mathematical model of contact between a deformable body and an obstacle, incorporating time-fractional derivatives.
Derived the variational formulation of the contact model.
Proved the existence of weak solutions for the mathematical model.
Analyzed a penalized version of the problem to show convergence of solutions as penalty parameter approaches zero.
Weak solutions were established in the variational formulation.
Solutions of the penalized model converge to those of the original variational inequality as penalty parameter tends to zero.

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Randomized trial analyzes mathematical contact model under unilateral constraints, suggesting convergence of solutions.

Cen et al. (2026) studied this question.

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