On Fractional Spherically Restricted Hyperbolic Diffusion Random Field

Nikolai Leonenko; Andriy Olenko; Jayme Vaz

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arXiv · 2310.03933

On Fractional Spherically Restricted Hyperbolic Diffusion Random Field

Nikolai Leonenko·Andriy Olenko·Jayme Vaz

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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.

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BibTeX RIS

Nikolai Leonenko, Andriy Olenko, Jayme Vaz. 2023-10-05. On Fractional Spherically Restricted Hyperbolic Diffusion Random Field. https://arxiv.org/abs/2310.03933

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