Vo Minh Tam, Jein-Shan Chen, Jann-Long Chern, Akiko Takeda, A fractional-order dynamical approach to vector equilibrium problems with partial order induced by a polyhedral cone
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DOI: 10.23952/jnva.9.2025.3.08
Volume 9, Issue 3, 1 June 2025, Pages 435-459
Abstract. In this paper, we propose a specific dynamical model for solving a class of vector equilibrium problems with partial order induced by a polyhedral cone which is generated by some matrix. Unlike the traditional dynamical models, it particularly possesses the feature of fractional-order system. The so-called Mittag-Leffler stability of the dynamical system is studied, which verifies the convergence to the solution of the corresponding vector equilibrium problems. This result is established by applying the techniques involving Caputo fractional derivatives, Lipschitz-type continuity and strong pseudo-monotonicity assumptions with partial ordering based on a polyhedral cone. Numerical implementations are demonstrated to illustrate the proposed approach. In addition, a real-world application to the general framework of vector network equilibrium models based on polyhedral cone ordering is presented.
How to Cite this Article:
V.M. Tam, J.S. Chen, J.L. Chern, A. Takeda, A fractional-order dynamical approach to vector equilibrium problems with partial order induced by a polyhedral cone, J. Nonlinear Var. Anal. 9 (2025), 435-459.