Abstract
We analyze a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation. We start our investigation by considering the linear case and the nonlinear case afterward. The linear case is discussed taking fractional time and spatial derivatives into account in a unified approach. We also discuss the modifications that emerge by employing simple drifts and the diffusion coefficient given by D(x,t)=D(t)|x|−θ. For the nonlinear case, we study scaling behavior of the time in connection with the asymptotic behavior for the solution of the nonlinear fractional diffusion equation.
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