Related papers: Fractional spherical random fields
Three theoretically plausible techniques to developing a fractional scalar field cosmological model are pointed in this paper; the time-dependent kernel weighted action being then selected. Upon this choice, we proceed to establish (i) a…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\alpha+1}$. It is shown that the equation of…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical singularities. In this article, we show $R$-sectoriality for the fractional powers of possibly…
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time…
Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.
We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure…
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as…