相关论文: On fractional powers of Bessel operators

Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…

This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral…

A recent paper by C.G. Kokologiannaki published in J. Math. Anal. Appl. \cite{Kolo:2012:BFI} gives some properties for ratios of modified Bessel functions and, in particular, some bounds. These bounds are said to improve the range of some…

Based on the need of studying the fractional boundary value problems by using variational methods, in this paper, we introduce a fundamental theory framework of fractional Sobolev space in one dimension, study the regularity of weak…

Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of Mellin convolutions and Bessel potential operators (BPOs). In contrast to the…

We present a general approach for evaluating a large variety of three-dimensional Fourier transforms. The transforms considered include the useful cases of the Coulomb and dipole potentials, and include situations where the transforms are…

The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such…

The generalized operators of fractional integration involving Appell's function $F_{3}(.) $ due to Marichev-Saigo-Maeda, is applied to the Bessel Struve kernel function $S_{\alpha }\left( \lambda z\right),\lambda ,z\in \mathbb{C}$ to obtain…

We introduce a fractional Bessel process with constant negative drift, defined as a time-changed Bessel process via the inverse of a stable subordinator, independent of the base process. This construction yields a model capable of capturing…

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…

In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…

We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and…

The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…

Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…

We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…

In this paper we derive the fractional power of the backward heat operator as a high dimensional limit of the fractional Laplacian. As applications, we derive Carleman type inequalities for fractional powers of the backward heat operator.

In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…

We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz potentials. These definitions rely on precise resolvent…

Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…

Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global H\"older and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup…