Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

Functionally Countable Spaces and Baire Functions

The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

A Brief Story about the Operators of the Generalized Fractional Calculus

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20