131 citations · 571 across the 40 of their papers we have counts for
41 papers
Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises
Z. Tomovski, K. Gorska, T. Pietrzak +2
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power…
The Havriliak-Negami and Jurlewicz-Weron-Stanislavsky relaxation models revisited: memory functions based study
K. Górska, A. Horzela, K. A. Penson
We provide a review of theoretical results concerning the Havriliak-Negami (HN) and the Jurlewicz-Weron-Stanislavsky (JWS) dielectric relaxation models. We derive explicit forms of…
Hausdorff moment problem for combinatorial numbers of Brown and Tutte: exact solution
K. A. Penson, K. Górska, A. Horzela +1
We investigate the combinatorial sequences introduced by W. G. Brown (1964) and W. T. Tutte (1980) appearing in enumeration of convex polyhedra. Their formula is $$A(M, n…
Non-Debye relaxations: The ups and downs of the stretched exponential vs Mittag-Leffler's matchings
K. Górska, A. Horzela, K. A. Penson
Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are got according to two distinct schemes: one can measure either the ti…
General approach to stochastic resetting
R. K. Singh, K. Gorska, T. Sandev
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times…
The Volterra type equations related to the non-Debye relaxation
K. Górska, A. Horzela
We investigate a possibility to describe the non-Debye relaxation processes using the Volterra-type equations with kernels given by the Prabhakar functions with the upper parameter…
On the Sheffer-type polynomials related to the Mittag-Leffler functions: applications to fractional evolution equations
K. Górska, A. Horzela, K. A. Penson +1
We present two types of polynomials related to the Mittag-Leffler function namely the fractional Hermite polynomial and the Mittag-Leffler polynomial. The first modifies the Hermit…
Some results on the complete monotonicity of the Mittag-Leffler functions of Le Roy type
K. Górska, A. Horzela, R. Garrappa
The paper by R. Garrappa, S. Rogosin, and F. Mainardi, entitled {\em On a generalized three-parameter Wright function of the Le Roy type} and published in [Fract. Calc. Appl. Anal.…
Can Umbral and -calculus be merged?
G. Dattoli, B. Germano, K. Górska +1
The -calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling…
On the complete monotonicity of the three parameter generalized Mittag-Leffler function
K. Górska, A. Horzela, A. Lattanzi +1
Using the Bernstein theorem we give a simple proof of the complete monotonicity of the three parameter generalized Mittag-Leffler function for and suita…
Composition law for the Cole-Cole relaxation and ensuing evolution equations
K. Górska, A. Horzela, A. Lattanzi
Physically natural assumption says that the any relaxation process taking place in the time interval , may be represented as a composition of pr…
Coherence, squeezing and entanglement -- an example of peaceful coexistence
K. Górska, A. Horzela, F. H. Szafraniec
After exhaustive inspection of bosonic coherent states appearing in physical literature two of us, Horzela and Szafraniec, came in 2012 to the reasonably general definition which r…
Mittag-Leffler function and fractional differential equations
K. Górska, A. Lattanzi, G. Dattoli
We adopt a procedure of operational-umbral type to solve the -dimensional fractional Fokker-Planck equation in which time fractional derivative of order () is…
Comments on the Properties of Mittag-Leffler Function
Giuseppe Dattoli, Katarzyna Gorska, Andrzej Horzela +2
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to de…
Holomorphic Hermite polynomials in two variables
K. Górska, A. Horzela, F. H. Szafraniec
Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials tr…
Theory of relativistic heat polynomials and one-sided Lévy distributions
G. Dattoli, K. Górska, A. Horzela +2
The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These type of equati…
The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions
K. Górska, A. Horzela, Ł. Bratek +2
We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern in the frequency domain with being some…
Relativistic Heat Equation via Lévy stable distributions: Exact Solutions
K. A. Penson, K. Górska, A. Horzela +1
We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corr…
The stretched exponential behavior and its underlying dynamics. The phenomenological approach
K. Górska, A. Horzela, K. A. Penson +2
We show that the anomalous diffusion equations with a fractional derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the Lévy stab…
Operational versus umbral methods and the Borel transform
G. Dattoli, E. Di Palma, E. Sabia +3
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special f…
On the properties of Laplace transform originating from one-sided Lévy stable laws
K. A. Penson, K. Górska
We consider the conventional Laplace transform of , denoted by with . For $0…
Photoluminescence decay of silicon nanocrystals and Lévy stable distributions
G. Dattoli, K. Gorska, A. Horzela +1
Recent experiments have shown that photoluminescence decay of silicon nanocrystals can be described by the stretched exponential function. We show here that the associated decay pr…
Squeezed States and Hermite polynomials in a Complex Variable
S. T. Ali, K. Gorska, A. Horzela +1
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related…
The Higher-Order Heat-Type Equations via signed Lévy stable and generalized Airy functions
K. Gorska, A. Horzela, K. A. Penson +1
We study the higher-order heat-type equation with first time and M-th spatial partial derivatives, M = 2, 3, ... . We demonstrate that its exact solutions for M even can be constru…