Fractional telegraph-type equations and hyperbolic Brownian motion

This paper is devoted to the interplay between time-fractional telegraph-type equations and processes defined on the nn-dimensional Poincaré half-space HnHn. We solve such equations and show that the solutions coincide with the law of the composition of a hyperbolic Brownian motion with the inverse of the sum of two independent stable subordinators. In the case n=3n=3, we obtain the explicit form of the solution of the above equation.