Fractional spherical random fields

TL;DR

This paper investigates fractional differential equations on the sphere, analyzing their solutions as time-dependent random fields, focusing on correlation functions and long-range dependence properties.

Contribution

It introduces a framework for fractional equations on the sphere and analyzes the correlation structure of their solutions as random fields.

Findings

Correlation functions exhibit specific long-range dependence patterns

Solutions demonstrate distinct temporal correlation decay

Framework applicable to spherical random field modeling

Abstract

In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of the random fields emerging in the analysis of the solutions of the fractional equations and examine their long-range behaviour.