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 n-dimensional Poincare half-space W. 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 = 3, we obtain the explicit form of the solution of the above equation. (c) 2014 Elsevier B.V. All rights reserved