Related papers: Fractional Operators in the Matrix Variate Case
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
We show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix-valued integral continued fractions. While these continued fractions are usual in the…
A widely used approach to compute the action $f(A)v$ of a matrix function $f(A)$ on a vector $v$ is to use a rational approximation $r$ for $f$ and compute $r(A)v$ instead. If $r$ is not computed adaptively as in rational Krylov methods,…
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…
We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$,…
The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results.
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of the Katugampola fractional integral of a univariate…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…