Generalized diffusion and asymptotics induced by Tsallis entropy

We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of the porous medium equations. We comment on the asymptotics of such solutions for large values of their spatial and temporal variables. We present conclusions for the generalised operations inspired by the Tsallis entropy composition and their relations to hyperbolicity.