Some identities on fractional integrals andintegral transforms

In this paper, we introduce various theorems that associate the generalized Riemann-Liouville fractional integral operator and the generalized Weyl fractional integral oper-ator with some well-known integral transforms including generalized Laplace transform,Widder potential transform, generalized Widder transform, Hankel transform and Besseltransform. We evaluate certain integrals of some elementary functions and some specialfunctions as applications of these theorems and their results.

PDF

___

[1]L. Debnath and D. Bhatta,Integral Transforms and Their Applications2ndEdition,Chapman and Hall CRC, Boca Raton, London and New York, 2007.
[2]A.N. Dernek and F. Aylıkçı,Identities for theLn-Transform, theL2n-Transform,and theP2n-Transform and Their Applications, Journal of Inequaities and SpecialFunctions,5(4), 1–16, 2014.
[3]A.N. Dernek and F. Aylıkçı,Some Results on thePν,2n,Kν,n,Hν,nIntegral trans-forms, Turkish J. Math.41, 337–349, 2017.
[4]A. Dernek, N. Dernek and O. Yürekli,Identities for the Henkel Transform and TheirApplications, J. Math. Anal. Appl.354, 165–176, 2009.
[5]A.N. Dernek, V. Kurt, Y. Şimşek and O. Yürekli,A generalization of Widder PotentialTransform and Applications, Integral Transforms Spec. Funct.22, 391–401, 2011.
[6]A.N. Dernek, H.M. Srivasta and O. Yürekli,Parseval-Goldstein Type Identities In-volving TheL4Transform andP4Transform and Their Applications, Integral Trans-forms Spec. Funct.18, (6), 397–408, 2007.
[7]A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi,Tables of Integral Trans-forms Vol: 1, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
[8]A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi,Tables of Integral Trans-forms Vol: 2, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
[9]I.S. Gradshteyn and I.M. Ryzhik,Table of Integrals, Series and Products, AcademicPress, New York, 1996.
[10]C. Li, D. Qian and Y. Chen,On Riemann Liouville and Caputo Derivatives, DiscreteDyn. Nat. Soc.2011, 2011.
[11]K.S. Miller and B. Ross,An Introduction to Fractional Calculus and Fractional Dif-ferential Equations, John Wiley-Interscience Publication, New York, Toronto, Singa-pore, 1993.
[12]I. Podlubny,An Introduction to Fractional Derivatives, Fractional Differential Equa-tions, to Methods of their Solution and Some of their Applications, Academic Press,San Diego and London, 1990.
[13]D.V. Widder,An Introduction to Transform Theory, Academic Press, New York,1971.
[14]O. Yürekli and I. Sadek,A Parseval-Goldstein Type Theorem on the Widder PotentialTransform and Its Applications, International J. Math. Math. Sci.14(3), 517–524,1991.
[15]O. Yürekli,Identities on Fractional Integrals and Various Integral Transforms, Appl.Math. Comput.187, 559–566, 2007.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

Arşiv