  Based on the continuous time random walk, we derive the Fokker-Planck
equations with Caputo-Fabrizio fractional derivative, which can effectively
model a variety of physical phenomena, especially, the material heterogeneities
and structures with different scales. Extending the discretizations for
fractional substantial calculus [Chen and Deng, \emph{ ESAIM: M2AN.}
\textbf{49}, (2015), 373--394], we first provide the numerical discretizations
of the Caputo-Fabrizio fractional derivative with the global truncation error
$\mathcal{O}(\tau^\nu)$ $ (\nu=1,2,3,4)$. Then we use the derived schemes to
solve the Caputo-Fabrizio fractional diffusion equation. By analysing the
positive definiteness of the stiffness matrices of the discretized
Caputo-Fabrizio operator, the unconditional stability and the convergence with
the global truncation error $\mathcal{O}(\tau^2+h^2)$ are theoretically proved
and numerical verified.
