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We explore the spatio-temporal evolution of solar flares by fitting a radialexpansion model $r(t)$ that consists of an exponentially growing accelerationphase, followed by a deceleration phase that is parameterized by thegeneralized diffusion function $r(t) \propto \kappa (t-t_1)^{\beta/2}$, whichincludes the logistic growth limit ($\beta=0$), sub-diffusion ($\beta = 0-1$),classical diffusion ($\beta=1$), super-diffusion ($\beta = 1-2$), and thelinear expansion limit ($\beta=2$). We analyze all M and X-class flaresobserved with GOES and AIA/SDO during the first two years of the SDO mission,amounting to 155 events. We find that most flares operate in the sub-diffusiveregime ($\beta=0.53\pm0.27$), which we interpret in terms of anisotropic chainreactions of intermittent magnetic reconnection episodes in a lowplasma-$\beta$ corona. We find a mean propagation speed of $v=15\pm12$ kms$^{-1}$, with maximum speeds of $v_{max}=80 \pm 85$ km s$^{-1}$ per flare,which is substantially slower than the sonic speeds expected for thermaldiffusion of flare plasmas. The diffusive characteristics established here (forthe first time for solar flares) is consistent with the fractal-diffusiveself-organized criticality (FD-SOC) model, which predicted diffusive transportmerely based on cellular automaton simulations.

The Spatio-Temporal Evolution of Solar Flares Observed with AIA/SDO: Fractal Diffusion, Sub-Diffusion, or Logistic Growth ?