Well-Posedness and Dependence on the Initial Value of the Time-Fractional Navier–Stokes Equations on the Heisenberg Group

In this paper, we examine the relevant properties of mild solutions to the fractional Navier–Stokes equations with respect to a time derivative of order \(0<\alpha <1\) $0<\alpha <1$ in a new spatial framework. On the Heisenberg group, these mild solutions are connected to the sublaplacian provided by the left-invariant vector fields. By applying appropriate conditions, we can obtain global and local mild solutions using the classical bilinear fixed point theorem. Furthermore, we have also established the dependence on the initial value of these mild solutions.