STUDY THE STABILITY OF THE FOURIER TRANSFORM OF THE VARIABLE-ORDER TIME FRACTIONAL SEMI-LINEAR DIFFUSION EQUATION

In this research, we present a finite difference scheme (FDS) aimed at exploring the linear time and space fractional advection equation.To approximate the fractional derivatives, we utilize the fractional Taylor series for u (x, t) at t j and x i .Our primary focus lies in constructing a numerical scheme (NS) for the mathematical model.Following this, we delve into an examination of the stability and convergence of our NS.Ultimately, we conduct numerical simulations of the fractional advection equation using the FDM across different fractional parameter values.The outcomes of these simulations demonstrate satisfactory convergence, thereby confirming the efficacy of the proposed algorithm.