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Title: Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?
Other Titles: Обобщения на дробното смятане, специалните функции и интегралните трансформации: Каква е връзката?
Authors: Kiryakova, Virginia
Keywords: Fractional Integrals and Derivatives
Generalized Hypergeometric Functions
Integral Transforms of Laplace Type
Issue Date: 2011
Publisher: Union of Bulgarian Mathematicians
Citation: Union of Bulgarian Mathematicians, Vol. 40, No 1, (2011), 42p-53p
Abstract: In this survey we briefly illustrate some of our contributions to the generalizations of the fractional calculus (analysis) as a theory of the operators for integration and differentiation of arbitrary (fractional) order, of the classical special functions and of the integral transforms of Laplace type. It is shown that these three topics of analysis are closely related and mutually induce their origins and developments. Due to the short space, we confine here only to survey the ideas of our recent contributions related to the title. Statements of the numerous results, their proofs, examples and applications can be found in Refs, like: [1]–[2], [5]–[7], [11]–[19]. *2010 Mathematics Subject Classification: 26A33, 33C60, 44A10, 44A40
Description: 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.
ISBN: 1313-3330
Appears in Collections:Mathematics and Education in Mathematics, 2011

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