Coupled system of fractional hemivariational inequalities with applications

References

• Pang JS, Stewart DE. Differential variational inequalities. Math Program. 2008;113(2):345–424.
   Web of Science ®Google Scholar
• Pang JS, Stewart DE. Solution dependence on initial conditions in differential variational inequalities. Math Program. 2009;116(1–2):429–460.
   Web of Science ®Google Scholar
• Chen X, Wang Z. Convergence of regularized time-stepping methods for differential variational inequalities. SIAM J Optim. 2013;23(3):1647–1671.
   Web of Science ®Google Scholar
• Gwinner J. On a new class of differential variational inequalities and a stability result. Math Program. 2013;139(1–2):205–221.
   Web of Science ®Google Scholar
• Loi NV. On two-parameter global bifurcation of periodic solutions to a class of differential variational inequalities. Nonlinear Anal Theory Methods Appl. 2015;122:83–99.
   Web of Science ®Google Scholar
• Liu ZH, Motreanu D, Zeng SD. On the well-posedness of differential mixed quasi-variational-inequalities. Topol Methods Nonlinear Anal. 2018;51:135–150.
   Web of Science ®Google Scholar
• Liu ZH, Migórski S, Zeng SD. Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces. J Differ Equ. 2017;263(7):3989–4006.
   Web of Science ®Google Scholar
• Panagiotopoulos PD. Nonconvex energy functions. Hemivariational inequalities and substationary principles. Acta Mechanic. 1983;42:160–183.
   Google Scholar
• Xu W, Huang ZP, Han WM, et al. Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration. Comput Math Appl. 2019;77(10):2596–2607.
   Web of Science ®Google Scholar
• Han WM, Sofonea M. Numerical analysis of hemivariational inequalities in contact mechanics. Acta Numerica. 2019;28:175–286.
   Web of Science ®Google Scholar
• Han WM, Migórski S, Sofonea M. Analysis of a general dynamic history-dependent variational-hemivariational inequality. Nonlinear Anal Real World Appl. 2017;36:69–88.
   Web of Science ®Google Scholar
• Xiao YB, Sofonea M. Generalized penalty method for elliptic variational-hemivariational inequalities. Appl Math Optim. 2021;83(2):789–812.
   Web of Science ®Google Scholar
• Migórski S, Ochal A, Sofonea M. Nonlinear inclusions and hemivariational inequalities: models and analysis of contact problems. New York: Springer; 2013.
   Google Scholar
• Migórski S, Pczka D. Almost history-dependent variational-hemivariational inequality for frictional contact problems. SIAM J Math Anal. 2020;52(5):4362–4390.
   Web of Science ®Google Scholar
• Xiao YB, Huang NJ, Wong MM. Well-posedness of hemivariational inequalities and inclusion problems. Taiwanese J Math. 2011;15(3):1261–1276.
   Web of Science ®Google Scholar
• Xiao YB, Yang X, Huang NJ. Some equivalence results for well-posedness of hemivariational inequalities. J Glob Optim. 2015;61(4):789–802.
   Web of Science ®Google Scholar
• Liu ZH, Zeng SD, Motreanu D. Partial differential hemivariational inequalities. Adv Nonlinear Anal. 2018;7(4):571–586.
   Web of Science ®Google Scholar
• Zeng SD, Migórski S, Van TN. A class of hyperbolic variational-hemivariational inequalities without damping terms. Adv Nonlinear Anal. 2022;11(1):1287–1306.
   Web of Science ®Google Scholar
• Migórski S, Han WM, Zeng SD. A new class of hyperbolic variational-hemivariational inequalities driven by non-linear evolution equations. Eur J Appl Math. 2021;32:59–88.
   Web of Science ®Google Scholar
• Liu ZH, Motreanu D, Zeng SD. Generalized penalty and regularization method for differential variational-hemivariational inequalities. SIAM J Optim. 2021;31(2):1158–1183.
   Web of Science ®Google Scholar
• Zeng SD, Migórski S, Liu ZH. Well-posedness, optimal control, and sensitivity analysis for a class of differential variational-hemivariational inequalities. SIAM J Optim. 2021;31(4):2829–2862.
   Web of Science ®Google Scholar
• Zeng SD, Migórski S, Khan AA. Nonlinear quasi-hemivariational inequalities: existence and optimal control. SIAM J Control Optim. 2021;59(2):1246–1274.
   Web of Science ®Google Scholar
• Li XW, Liu ZH. Sensitivity analysis of optimal control problems described by differential hemivariational inequalities. SIAM J Control Optim. 2018;56(5):3569–3597.
   Web of Science ®Google Scholar
• Migórski S, Zeng SD. A class of differential hemivariational inequalities in Banach spaces. J Global Optim. 2018;72(4):761–779.
   Web of Science ®Google Scholar
• Han JF, Migórski S, Zeng HD. Weak solvability of a fractional viscoelastic frictionless contact problem. Appl Math Comput. 2017;303:1–18.
   Web of Science ®Google Scholar
• Zeng SD, Migórski S. A class of time-fractional hemivariational inequalities with application to frictional contact problem. Commun Nonlinear Sci Numer Simul. 2018;56:34–48.
   Web of Science ®Google Scholar
• Zeng SD, Liu ZH, Migórski S. A class of fractional differential hemivariational inequalities with application to contact problem. Zeitschrift für angewandte Mathematik und Physik. 2018;69(2):36.
   Web of Science ®Google Scholar
• Cen JX, Liu YJ, Nguen VT, et al. Existence of solutions for fractional evolution inclusion with application to mechanical contact problems. Fractals. 2021;29(08):Article ID 2140036.
   Web of Science ®Google Scholar
• Hao JW, Wang JR, Han JF. History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems. Math Mech Solids. 2022;27(6):1032–1052.
   Web of Science ®Google Scholar
• Weng YH, Chen T, Li XS, et al. Rothe method and numerical analysis for a new class of fractional differential hemivariational inequality with an application. Comput Math Appl. 2021;98:118–138.
   Web of Science ®Google Scholar
• Weng YH, Li XS, Huang NJ. A fractional nonlinear evolutionary delay system driven by a hemi-variational inequality in Banach spaces. Acta Math Sci. 2021;41(1):187–206.
   Web of Science ®Google Scholar
• Zeng SD, Cen JX, Atangana A, et al. Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian. Zeitschrift für angewandte Mathematik und Physik. 2021;72(1):30.
   Web of Science ®Google Scholar
• Atangana A. Fractional discretization: the African's tortoise walk. Chaos Solitons Fract. 2020;130:Article ID 109399.
   Web of Science ®Google Scholar
• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.
   Google Scholar
• Zhou Y, Jiao F. Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal Real World Appl. 2010;11(5):4465–4475.
   Web of Science ®Google Scholar
• Atangana A, Shafiq A. Differential and integral operators with constant fractional order and variable fractional dimension. Chaos Solitons Fract. 2019;127:226–243.
   Web of Science ®Google Scholar
• Luo DF, Tian MQ, Zhu QX. Some results on finite-time stability of stochastic fractional-order delay differential equations. Chaos Solitons Fract. 2022;158:Article ID 111996.
   Web of Science ®Google Scholar
• Wang X, Luo DF, Zhu QX. Ulam-Hyers stability of Caputo type fuzzy fractional differential equations with time-delays. Chaos Solitons Fract. 2022;156:Article ID 111822.
   Web of Science ®Google Scholar
• Denkowski Z, Migórski S, Papageorgiou NS. An introduction to nonlinear analysis: applications. Boston/Dordrecht/London: Kluwer Academic Publishers; 2003.
   Google Scholar
• Carstensen C, Gwinner J. A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems. Annali di Matematica Pura ed Applicata. 1999;177(1):363–394.
   Web of Science ®Google Scholar
• Barboteu M, Hoarau-Mantel TV, Sofonea M. On the frictionless unilateral contact of two viscoelastic bodies. J Appl Math. 2003;11:575–603.
   Google Scholar