On Fractional Spherically Restricted Hyperbolic Diffusion Random Field

TL;DR

This paper explores solutions to a fractional hyperbolic diffusion equation, analyzing their properties as random fields with spherical restrictions, spectral representations, and numerical insights into how fractional orders influence their covariance and structure.

Contribution

It introduces a comprehensive analysis of fractional hyperbolic diffusion solutions as random fields with spherical restrictions, including spectral representations and numerical assessments of fractional order effects.

Findings

Spectral representations of the random fields are derived.

The covariance structure depends on the fractional derivative orders.

Numerical examples illustrate the theoretical results.

Abstract

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random fields and their spherical restrictions are studied. The spectral representations of these fields are derived and the associated angular spectrum is analysed. The obtained mathematical results are illustrated by numerical examples. In addition, the numerical investigations assess the dependence of the covariance structure and other properties of these fields on the orders of fractional derivatives.