Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption

Abstract

We analyze a nonlinear fractional diffusion equation with absorption by employing fractional spatial derivatives and obtain some more exact classes of solutions. In particular, the diffusion equation employed here extends some known diffusion equations such as the porous medium equation and the thin film equation. We also discuss some implications by considering a diffusion coefficient $\mathcal{D}(x,t)=\mathcal{D}(t)|x{|}^{\ensuremath{-}\ensuremath{\theta}}$ $(\ensuremath{\theta}\ensuremath{\in}\mathcal{R})$ and a drift force $F=\ensuremath{-}{k}_{1}{(t)x+k}_{\ensuremath{\alpha}}x|x{|}^{\ensuremath{\alpha}\ensuremath{-}1}.$ In both situations, we relate our solutions to those obtained within the maximum entropy principle by using the Tsallis entropy.