A note on generalized fractional diffusion equations on Poincar\`e half plane
Abstract
In this paper we study generalized time-fractional diffusion equations on the Poincar\`e half plane H2+. The time-fractional operators here considered are fractional derivatives of a function with respect to another function, that can be obtained by starting from the classical Caputo-derivatives essentially by means of a deterministic change of variable. We obtain an explicit representation of the fundamental solution of the generalized-diffusion equation on H2+ and provide a probabilistic interpretation related to the time-changed hyperbolic Brownian motion. We finally include an explicit result regarding the non-linear case admitting a separating variable solution.
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