Identities on fractional integrals and various integral transforms
type: Item
instance of: scholarly article
title: Identities on fractional integrals and various integral transforms
zbMATH Open document ID: 1127.44001
published in: Applied Mathematics and Computation
publication date: 2007-06-13T00:00:00Z
review text: There is an important property relating the Laplace transform to integration, \(L\{\frac{f(t)}{t}\}=\int^\infty_sF(x)dx\). The author extends this identity to Weyl's fractional integration. In this spirit, he provides several interesting theorems relating the Weyl fractional integral and the Riemann-Liouville fractional integral to some classical integral transforms -- the Laplace, Stieltjes, Hankel, Widder potential transforms and the \(K\)-transform. As application, some interesting infinite integrals are evaluated involving elementary and special functions.
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 5163964
zbMATH Keywords: Parseval-Goldstein type of identities
zbMATH Keywords: Riemann-Liouville fractional integral
zbMATH Keywords: Weyl fractional integral
zbMATH Keywords: fractional derivatives
zbMATH Keywords: Laplace transform
zbMATH Keywords: Widder potential transform
zbMATH Keywords: Stieltjes transform
zbMATH Keywords: generalized Stieltjes transform
zbMATH Keywords: Hankel transform
zbMATH Keywords: \(K\)-transform
zbMATH Keywords: Bessel functions
zbMATH Keywords: modified Bessel functions of the third kind
zbMATH Keywords: exponential integral function
zbMATH Keywords: error function
zbMATH Keywords: complementary error function
author: Osman Yürekli
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: j.amc.2006.09.001
OpenAlex ID: W1974795389
cites work: Q5831457
cites work: Q3671491
cites work: A theorem on the glasser transform and its applications
cites work: Q4777828
cites work: A theorem on Widder's potential transform and its applications
cites work: A theorem on a stieltjes-type integral transform and its applications
cites work: Some inversion formulas for the widder potential transform
cites work: A Parseval-type Theorem Applied to Certain Integral Transforms
cites work: A theorem on the generalized Stieltjes transform and its applications
cites work: New identities involving the Laplace and the \({\mathcal L}_2\)-transforms and their applications
DOI: 10.1016/J.AMC.2006.09.001
Recommended article: Some identities on fractional integrals and integral transforms
Recommended article: Q3585892
Recommended article: Q3345254
Recommended article: Q4233623
Recommended article: Q5365441
Recommended article: Q3514189
Recommended article: On some fractional integrals and their applications
Recommended article: Q4288757
Recommended article: Fractional integral transform and application
description: scientific article; zbMATH DE number 5163964