An approximation for the conformable time-space fractional diffusion equation

The present paper suggests a finite difference method to approximate the one-dimensional time-space fractional diffusion equation, with the initial and boundary conditions, that employs the conformable fractional derivative. The stability and convergence of this approach are proved, and numerical experiments confirm its second-order accuracy. One of the advantages of this method is that it can be readily extended to the two or three-dimensional time-space fractional diffusion equation that uses the conformable fractional derivative.