Sergei Rogosin

Mittag-Leffler Functions, Related Topics and Applications

As a result of researchers and scientists increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

On the generalized mittag-leffler type functions

The paper is devoted to the study of the properties of the special functions generalizing the Mittag-Leffler type functions. The order and type of such entire functions are evaluated and recurrence relations are given. Connections with hypergeometric functions are discussed and differentiation formulae are proved.

Multi-parametric mittag-leffler functions and their extension

This paper surveys one of the last contributions by the late Professor Anatoly Kilbas (1948–2010) and research made under his advisorship. We briefly describe the historical development of the theory of the discussed multi-parametric Mittag-Leffler functions as a class of the Wright generalized hypergeometric functions. The method of the Mellin-Barnes integral representations allows us to extend the considered functions to the case of arbitrary values of parameters. Thus, the extended Mittag-Leffler-type functions appear. The properties of these special functions and their relations to the fractional calculus are considered. Our results are based mainly on the properties of the Fox H-functions, as one of the widest class of special functions.

George William Scott Blair { the pioneer of fractional calculus in rheology

The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by the rheological society and is adopted and generalized by his successors. Further development of this branch of Science is briefly described in this article too.

Effective conductivity of a composite material with non-ideal contact conditions

The effective conductivity of 2D doubly periodic composite materials with circular disjoint inclusions under non-ideal contact conditions on the boundary between material components is found. The obtained explicit formula for the effective conductivity contains all parameters of the considered model, such as the conductivities of matrix and inclusions, resistance coefficients, radii and centres of the inclusions and also the values of special Eisenstein functions. The method of functional equations is used to analyse the conjugation problem for analytic functions which is equivalently derived from the initial problem. Existence and uniqueness for the solution of the problem is obtained by using a reduction to a certain mixed boundary value problem for analytic functions in special functional spaces.

On the Creation of a New Diagnostic Model for Fetal Well-Being on the Base of Wavelet Analysis of Cardiotocograms

The article is devoted to the description of the results of wavelet analysis of fetal heart rate detecting by cardiotocography method. A number of conclusions are made on the base of such an analysis.It is a part of the research program of creation of a new diagnostic model estimating fetal conditions in antepartum period.

Advances in Applied Analysis

Introduction.- Kisil, Vladimir V.: Erlangen Program at Large: Brief Outline.- Laurincikas, A.: The Riemann zeta-function: approximation of analytic functions.- Luchko, Yury: Anomalous diffusion: models, their analysis, and interpretation.- Mityushev, Vladimir, V.: R-linear and Riemann-Hilbert problems for multiply connected domains.- Plaksa, S. A.: Commutative algebras associated with classic equations of mathematical physics.- Rogosin, Sergei V.: 2D Free Boundary Value Problems.

Analytical methods for heat conduction in composites

Abstract Analytical methods unifying the study of heat conduction in various type of composite materials are described. Analytical formulas for the effective (macroscopic) conductivity tensor are presented.

An asymptotic method of factorization of a class of matrix-functions

A novel method of asymptotic factorization of n×n matrix functions is proposed. The considered class of matrices is motivated by certain problems originated from the elasticity theory. An example is constructed to illustrate efficiency of the proposed procedure. The quality of approximation and the role of the chosen small parameter are discussed.

Professor Rudolf Gorenflo and his contribution to fractional calculus

This paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo — a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fractional Calculus and its applications is highlighted.