The fractional diffusion equation is

, where the

is the Riemann–Liouville derivative of order

,

, is solved numerically by means of the fractional difference weighted-average methods (or

methods) discussed in [1]. When

, the equation is just the normal diffusion equation and these methods become normal weighted-average methods [2]. Depending on the value of the weight factor

, the method can be fully implicit when

, or fully explicit when

. The fractional Crank–Nicolson method for

, or for other values of

, is a generic

-weighted-average method. It is also determined whether the stability criterion of equation (35) of [1] is also satisfied. The size

of the timestep and the number

of timesteps can be chosen. The diffusion constant

and the space discretization

* *are fixed to 1 and

with

, respectively. When the "normal solution" checkbox is checked, the normal diffusion solution (

) is also plotted (orange points). The broken lines are to guide the eye. The values of the numerical solutions are shown when the mouse pointer is over the points.

[2] K. W. Morton and D. F. Mayers,

*Numerical Solution of Partial Differential Equations*, Cambridge: Cambridge University Press, 1994.