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

Abstract

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 β∈(0,1). In Hγ,℘, 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.

Keywords

• Navier–Stokes equation
• Caputo fractional derivative
• Mittag–Leffler function
• mild solution
• fuzzy fractional differential equation
• regularity