Related papers: Fractional operators via analytic interpolation of…

The main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional…

Let $\alpha$ be a real number greater than $1$. We establish an effective lower bound for the distance between an integral power of $\alpha$ and its nearest integer.

This paper uses cybernetic approach to study behavior of the Riemann zeta function. It is based on the elementary cybernetic concepts like feedback, transfer functions, time delays, PI (Proportional--Integral) controllers or FOPDT (First…

Let $L$ be a closed, densely defined operator on $L^2(\mathbb{R}^n)$ satisfying suitable $L^p-L^q$ off-diagonal estimates of order $\kappa > 0$. This paper aims to investigate the two-weight estimate and the Bloom weighted estimate for the…

We investigate solutions to the functional equation $f(f(x)) = e^x$, which can be interpreted as the problem of finding a half iterate of the exponential map. While no elementary solution exists, we construct and analyze non-elementary…

We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.

We show that highly accurate approximations can often be obtained from constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained…

We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…

In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…

We use symmetric Poisson-Schwarz formulas for analytic functions $f$ in the half-plane ${Re}(s)>\frac12$ with $\bar{f(\bar{s})}=f(s)$ in order to derive factorisation theorems for the Riemann zeta function. We prove a variant of the…

Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating…

The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…

Via chirp functions from fractional Fourier transforms, the authors introduce fractional Riesz potentials related to chirp functions, establish their relations with fractional Fourier transforms, fractional Laplace operators related to…

Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…

In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative…

First, we establish the theory of fractional powers of first order differential operators with zero order terms, obtaining PDE properties and analyzing the corresponding fractional Sobolev spaces. In particular, our study shows that…

In this paper we consider some rational approximations to the fractional powers of self-adjoint positive operators, arising from the Gauss-Laguerre rules. We derive practical error estimates that can be used to select a priori the number of…

This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…

We describe a numerical algorithm for evaluating the numbers of roots minus the number of poles contained in a region based on the argument principle with the function of interest being written as a Mellin transformation of a usually…

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl…