Related papers: Simplified Inequalities for Fractional Wavelet Fra…
In this paper, we establish several inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…
We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter…
In this paper, some new inequalities of the Hermite-Hadamard type for h-convex functions via Riemann-Liouville fractional integral are given.
In this paper, scattering of incident plane waves from rough surfaces have been modeled in a fractional space. It is shown how wave scattering from a rough surface, could be a simple reflection problem in a fractional space. In the integer…
In this paper we study the obstacle problems for the Navier (spectral) fractional Laplacian $\left(-\Delta_\Omega\right)^{\!s}$ of order $s\in(0,1)$, in a bounded domain $\Omega\subset\mathbb R^n$.
In this article we study the fractional Hankel transform and its inverse on certain Gel'fand-Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of…
In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
We prove Hardy-type inequalities for a fractional Dunkl--Hermite operator which incidentally give Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use $h$-harmonic expansions to reduce the problem in the…
A phase space description of the fractional Talbot effect, occurring in a one-dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at…
Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.
We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.
There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on $L^2(\R)$, including the…
In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical…
Fractional Sobolev spaces $\widehat{H}^s(\mathbb{R})$ have been playing important roles in analysis of many mathematical subjects. In this work, we re-consider fractional Sobolev spaces under the perspective of fractional operators and…
The aim of this paper is to give a wavelet series representation of Linear Multifractional Stable Motion (LMSM in brief), which is more explicit than that introduced in (Ayache & Hamonier 2012). Instead of using Daubechies wavelet, which is…
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The…