Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Fractional Differential Equations

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

The flow of homogeneous fluids through porous media: analogies with other physical problems

Consider the function defined for $\alpha _{1},\ \alpha _{2} \in \mathbb{R}$ (α 1 2 +α 2 2 ≠ 0) and $\beta _{1},\beta _{2} \in \mathbb{C}$ by the series 

$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$

(6.1.1)

Such a function with positive α 1 > 0, α 2 > 0 and real $\beta _{1},\beta _{2} \in \mathbb{R}$ was introduced by Dzherbashian [Dzh60].

Multi-index Mittag-Leffler Functions

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.

Mittag-Leffler Functions, Related Topics and Applications

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

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Stability of Fractional Order Systems

A HISTORICAL SURVEY NOTATIONS AND AUXILIARY RESULTS Geometry of Complex Plane Functional Spaces Operator Equations in Functional Spaces Properties of Analytic and Harmonic Functions Cauchy-Type Integral and Singular Integrals Schwarz Operator C-Linear Conjugation Problem Riemann-Hilbert Boundary Value Problem Entire Function Conformal Mappings R-Linear Problem and its Applications Notes and Comments NONLINEAR BOUNDARY VALUE PROBLEMS Conjugation Problem of Power Type Problem of Multiplication Type Entire Functions Methods General Riemann-Hilbert Problem of Power Type The Modulus Problem and its Generalization Linear Fractional Problem Cherepanov's Mixed Problem Notes and Comments METHOD OF FUNCTIONAL EQUATIONS Dirichlet Problem for a Doubly Connected Domain A Nonlinear Boundary Value Problem Linear Functional Equations Harmonic Measures and Schwarz Operator Linear Riemann-Hilbert Porblem Poincare Series Mixed Problem for Multiply Connected Domains Circular Polygons with Zero Angles Generalized Method of Schwarz and other Methods Notes and Comments NONLINEAR PROBLEMS OF MECHANICS Steady Heat Conduction: Nonlinear Composites Linearized Problem Constructive Solution to Integral Equations Composite Materials with Reactive Inclusions Steady Heat Conduction on Configurations An Elastic Problem for Composite Materials Plane Stokes Flow Notes and Comments BIBLIOGRAPHY INDEX

Constructive methods for linear and nonlinear boundary value problems for analytic functions : theory and applications

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.

Sergei Rogosin

Papers

Multi-index Mittag-Leffler Functions

Mittag-Leffler Functions, Related Topics and Applications

Stability of Fractional Order Systems

Constructive methods for linear and nonlinear boundary value problems for analytic functions : theory and applications

On the generalized mittag-leffler type functions