Local and Global Mild Solution for Gravitational Effects of the Time Fractional Navier–Stokes Equations

The gravitational effect is a physical phenomenon that explains the motion of a conductive fluid flowing under the impact of an exterior gravitational force. In this paper, we work on the Navier–Stokes equations (NSES) of the fluid flowing under the impact of an exterior gravitational force inclined at an angle of 45∘ with A time-fractional derivative of order β∈(0,1). To encourage anomalous diffusion in fractal media, we apply these equations. In Hδ,r, we prove the existence and uniqueness of local and global mild solutions. Additionally, we provide moderate local solutions in Jr. Additionally, we establish the regularity and existence of classical solutions to these equations in Jr.