Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation

In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis.