Spectral Analysis of Fractional Hyperbolic Diffusion Equations with Random Data

Abstract

The paper studies the fundamental solutions to fractional in time hyperbolic diffusion equation or telegraph equations and their properties. Then it derives the exact solutions of the fractional hyperbolic diffusion equation with random data in terms of series expansions of isotropic in space spherical random fields on the unit sphere. Numerical illustration are presented to illustrate the theoretical results.