Local and Global Existence and Uniqueness of Solution for Time-Fractional Fuzzy Navier-Stokes Equations

Navier-Stokes (NS) equation, in fluid mechanics, is a partial differential equation that describes the flow of incompressible fluids. We study the fractional derivative by using fractional differential equation by using a mild solution. In this work, anomaly diffusion in fractal media is simulated using the Navier-Stokes equations (NSEs) with time-fractional derivatives of order beta is an element of (0, 1). In H-gamma,H-rho, we prove the existence and uniqueness of local and global mild solutions by using fuzzy techniques. Meanwhile, we provide a local moderate solution in Banach space. We further show that classical solutions to such equations exist and are regular in Banach space.