I am very new to the subject of fractional derivatives which arise while characterizing the anomalous transport of passive scalar in turbulence.
I have found an equation of the following form, to describe such anomalous transport, which I have to solve numerically, $$\partial_{t}f(x,t)=kD^{\alpha}_{|x|}f(x,t)+g(x,t)$$ where $k$ is some constant, $D^{\alpha}_{|x|}$ is symmetric Riesz fractional derivative of order $\alpha$ and $g(x,t)$ is a source/sink term. The numerical algorithm that I can find are too mathematically abstract for me, therefore it would be of great help if anyone could sketch out the basic ideas behind constructing numerical algorithms for such equations.