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Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation? Обобщения на дробното смятане, специалните функции и интегралните трансформации: Каква е връзката?

Kiryakova, Virginia — 2011

Union of Bulgarian Mathematicians

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. In this survey...

A Brief Story about the Operators of the Generalized Fractional Calculus

Kiryakova, Virginia — 2008

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20 In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized hypergeometric functions, including...

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

Kiryakova, Virginia — 2006

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35 Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, two operators...

On Some of Professor Peter Rusev's Contributions

Kiryakova, Virginia — 2012

Mathematica Balkanica New Series

MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05 The 6th International Conference "Transform Methods and Special Functions' 2011", 20 - 23 October 2011 was dedicated to the 80th anniversary of Professor Peter Rusev, as one of the founders of this series of international meetings in Bulgaria, since 1994. It is a pleasure to congratulate the Jubiliar on behalf of the Local Organizing Committee and International Steering Committee, and to present shortly some of his life...

A Poster about the Old History of Fractional Calculus

Tenreiro Machado, J.Kiryakova, VirginiaMainardi, Francesco — 2010

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

Hankel type integral transforms connected with the hyper-Bessel differential operators

Yurii LuchkoVirginia Kiryakova — 2000

Banach Center Publications

In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 B : = x - β j = 1 m ( x ( d / d x ) + β γ j ) , β>0, γ j R , j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms...

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