Related papers: Fractional spherical random fields
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…
We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.
We study a compound Poisson random field on plane and examine its various fractional variants. We derive the distributions of these random fields and in some particular cases, obtain their associated system of governing differential…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…