Existence and Convergence of Solutions to the ψ‐Caputo Fractional Navier–Stokes–Voigt Equations Via the Rothe Method

ABSTRACT This paper investigates the existence and convergence of solutions for the ‐Caputo fractional Navier–Stokes–Voigt (N–S–V) equations, a model describing the dynamics of viscoelastic incompressible fluids. The study addresses the solvability of these equations, which involve time‐fractional integrals and are governed by weakly continuous, nonlinear operators. By employing the Rothe method combined with surjective results for weakly continuous operators, we establish the existence of weak solutions. Furthermore, we prove that these weak solutions converge to those of the classical Navier–Stokes equations as the elasticity parameter approaches zero.