<p>This paper investigates a class of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_836_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional differential hemivariational inequalities (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_836_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-CFDHI). The analysis confirms the existence and uniqueness of solutions by applying the Rothe method alongside surjectivity properties of multivalued pseudomonotone operators. The theoretical insights are then applied to a nonlinear thermo-viscoelastic contact problem governed by a fractional Kelvin–Voigt constitutive model with adhesion effects.</p>

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Fractional differential hemivariational inequalities with applications

  • Zakaria Faiz,
  • Hicham Benaissa

摘要

This paper investigates a class of \(\psi \) ψ -Caputo fractional differential hemivariational inequalities ( \(\psi \) ψ -CFDHI). The analysis confirms the existence and uniqueness of solutions by applying the Rothe method alongside surjectivity properties of multivalued pseudomonotone operators. The theoretical insights are then applied to a nonlinear thermo-viscoelastic contact problem governed by a fractional Kelvin–Voigt constitutive model with adhesion effects.