Related papers: Complex-Order Scale-Invariant Operators and Self-S…
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.
Complex systems are composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…
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…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
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…
We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
We introduce a continuous-order integral analog of the Maclaurin expansion that reconstructs analytic functions from fractional derivative data. The operator integrates over continuous order, replacing the discrete sum of integer…
We study a system of partial differential equations defined by commuting family of differential operators with regular singularities. We construct ideally analytic solutions depending on a holomorphic parameter. We give some explicit…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…