A Second-order Accurate Scheme For Two-dimensional Space Fractional Diffusion Equations With Time Caputo-fabrizio Fractional Derivative

We provide and analyze a second order scheme for the model describing the func-tional distributions of particles performing anomalous motion with exponential Debye pattern and no-time-taking jumps eliminated,and power-law jump length.The equation is derived by continuous time random walk model,being called the space fractional d-iffusion equation with the time Caputo-Fabrizio fractional derivative.The designed schemes are unconditionally stable and have the second order global truncation error with the nonzero initial condition,being theoretically proved and numerically verified by two methods(a prior estimate with L~2-norm and mathematical induction with l_? norm).Moreover,the optimal estimates are obtained.