Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

An Adaptive Quadrilateral Mesh in Curved Domains

An nonlinear elliptic system for generating adaptive quadrilateral meshes in curved domains is presented. The presented technique has been implemented in the C++ language with the help of the standard template library. The software package writes the converged meshes in the GMV and the Matlab formats. Grid generation is the first very important step for numerically solving partial differential equations. Thus, the presented C++ grid generator is extremely important to the computational science community.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

PREFACE

The Conference on Partial Differential Equations and Applications, Sofia, September 14–16, 2011 (In honor of 65-th Anniversary of Professor Petar Popivanov) took place in the premises of the Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS). The conference was organized by the Section “Differential Equations and Mathematical Physics” of IMI with the participation of research groups on PDE from Universit`a di Cagliari and Universit`a di Torino (Italy), with the organizing committee – N. Kutev (IMI–BAS) – chair, G. Boyadzhiev (IMI–BAS) – secretary, T. Gramchev (Univ. Cagliari) and A. Oliaro (Univ. Torino) – members, and thefollowing program/scientific committee: T. Gramchev (chair), N. Kutev (IMI–BAS), L. Rodino (Universit`a di Torino), M. Ruzhansky (Imperial College London), A. Slavova (IMI–BAS), C. Van Der Mee (Universit`a di Cagliari).

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes

2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.

Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier

2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.