\(N\)-fractional calculus of products of some power functions and some doubly infinite sums
type: Item
instance of: scholarly article
title: \(N\)-fractional calculus of products of some power functions and some doubly infinite sums
zbMATH Open document ID: 1122.26005
author: Katsuyuki Nishimoto
published in: Applied Mathematics and Computation
publication date: 2007-06-13T00:00:00Z
review text: The author has studied fractional calculus extensively through his famous five volume series of books [``Fractional calculus''. Vol. 1 (1984; Zbl 0605.26006); Vol. 2 (1987; Zbl 0702.26011); Vol. 3 (1989; Zbl 0798.26005); Vol. 4 (1991; Zbl 0798.26006); Vol. 5 (1996; Zbl 0911.26004)] published during the period 1984--1996 and calls it \(N\)-fractional calculus. In the present paper he first obtains \(N\)-fractional calculus of products of some power functions. Next, he gives doubly infinite, finite and mixed infinite sums with the help of results obtained earlier. Finally, he presents direct calculation of doubly infinite sums without making use of \(N\)-fractional calculus.
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 5163939
zbMATH Keywords: fractional calculus
zbMATH Keywords: \(N\)-fractional calculus operator
reviewed by: K. C. Gupta
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.131
OpenAlex ID: W2039852247
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DOI: 10.1016/J.AMC.2006.08.131
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description: scientific article; zbMATH DE number 5163939