An approximation for the conformable time-space fractionaldiffusion equation

The present paper suggests a finite difference method to approximate the onedimensionaltime-space fractional diffusion equation, with the initial and boundaryconditions, that employs the conformable fractional derivative. The stability and convergenceof this approach are proved, and numerical experiments confirm its secondorderaccuracy. One of the advantages of this method is that it can be readily extendedto the two or three-dimensional time-space fractional diffusion equation that uses theconformable fractional derivative.

Keywords:

Time-space fractional diffusion equation , Conformable derivative , Crank-Nicolson method , Convergence , Stability