Related papers: A quaternionic proportional fractional Fueter-type…
We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to Haar measure over classical groups. Although a…
Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized…
This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann-Liouville and Caputo definitions, we discuss when the fractional derivative and when…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the…
By exploiting the Fueter theorem, we give new formulas to compute zonal harmonic functions in any dimension. We first give a representation of them as a result of a suitable ladder operator acting on the constant function equal to one.…
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted…
We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…
An analogue of the Fourier transform will be introduced for all square integrable continuous martingale processes whose quadratic variation is deterministic. Using this transform we will formulate and prove a stochastic Heisenberg…
In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…
The $k$-Cauchy-Fueter operators, $k=0,1,\ldots$, are quaternionic counterparts of the Cauchy-Riemann operator in the theory of several complex variables. The weighted $L^2$ method to solve Cauchy-Riemann equation is applied to find the…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.
In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators…
In this work we show that it is possible to calculate the fractional integrals and derivatives of order $\alpha$ (using the Riemann-Liouville formulation) of power functions $\left( t-\ast\right) ^{\beta}$ with $\beta$ being any real value,…