Mild Solutions for the Time-Fractional Navier-Stokes Equations with MHD Effects

Abstract

Recently, various techniques and methods have been employed by mathematicians to solve specific types of fractional differential equations (FDEs) with symmetric properties. The study focuses on Navier-Stokes equations (NSEs) that involve MHD effects with time-fractional derivatives (FDs). The (NSEs) with time-FDs of order β∈(0,1) are investigated. To facilitate anomalous diffusion in fractal media, mild solutions and Mittag-Leffler functions are used. In Hδ,r, the existence, and uniqueness of local and global mild solutions are proved, as well as the symmetric structure created. Moderate local solutions are provided in Jr. Moreover, the regularity and existence of classical solutions to the equations in Jr. are established and presented.

New Solutions of Time- and Space-Fractional Black–Scholes European Option Pricing Model via Fractional Extension of He-Aboodh Algorithm

“…Galerkin method [21], implicit fnite diference scheme [22], Adomian decomposition method [23], Crank-Nicolson scheme [24], homotopy perturbation method [25], backward Euler method [26], diferential transform method [27], and stabilized meshless technique [28] are some of them. Many of these approaches have been utilized for the numerical solution of fractional diferential equations including the Navier-Stokes equation [29,30], Schrödinger equation [31], COVID-19 model [32], Kundu-Mukherjee-Naskar equation [33], and Black-Scholes model [34]. Chen et al [35] employed a Laguerre neural network for generalized Black-Scholes models.…”