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...
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...
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...
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...
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22
In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major
contributions during the period 1966-2010.
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.
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 , β>0, , 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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