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