Fractional and nonlinear diffusion equation: additional results (original) (raw)

We investigate the solutions of a generalized di usion equation which extends some known equations such as the fractional di usion equation and the porous medium equation. We start our study by considering the linear case and the nonlinear case afterward. The linear case is analyzed taking fractional time and spatial derivatives into account. In this context, we also discuss the modiÿcations that emerge by considering a di usion coe cient given by D(x)˙|x| −Â. For the nonlinear case accomplishing the fractional time derivative, we discuss scaling behavior of the time and the asymptotic for the solution of the nonlinear fractional di usion equation. In this case, the connection between the asymptotic solution found here and the nonextensive Tsallis statistics is performed.