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Abderrahmane Oultou, Hicham Benaissa, A coupled system of Hilfer fractional differential and history-dependent hemivariational inequalities

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DOI: 10.23952/asvao.8.2026.3.01
Volume 8, Issue 3, 1 December 2026, Pages 271-292

 

Abstract. This paper studies a novel coupled system consisting of a Hilfer fractional differential equation and two dynamic history-dependent hemivariational inequalities. The proposed framework models complex interactions involving memory effects, nonconvex constraints, and coupled evolutionary processes. By applying Rothe’s semi-discretization method together with surjectivity results for pseudomonotone operators, we establish the existence of solutions under suitable assumptions. The analysis provides constructive discrete approximations that converge to a solution of the original continuous problem, thereby extending the theory of differential variational inequalities to fractional-order systems with nonsmooth and history-dependent dynamics.

 

How to Cite this Article:
A. Oultou, H. Benaissa, A coupled system of Hilfer fractional differential and history-dependent hemivariational inequalities, Appl. Set-Valued Anal. Optim. 8 (2026), 271-292.