Reduction of Time‐Fractional Stokes–Voigt Equations with Nonlinear Friction Law in a Thin Layer

ABSTRACT For , we analyze the system of the time‐fractional Stokes–Voigt equations in a three‐dimensional thin domain with Tresca friction law where the velocity, the pressure and , denotes the Riemann‐Liouville fractional derivatives of order , respectively. We begin by presenting the mathematical formulation and the associated weak form of the problem under consideration. Subsequently, we perform an asymptotic analysis in the regime where one geometrical dimension of the domain shrinks to zero. This leads us to derive the corresponding limit problem, which includes a specific form of the Reynolds‐type equation.