Fractional calculus operators and their applications involving power functions and summation of series

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dc.contributor.author Chen, M-P.
dc.contributor.author Srivastava, H.M.
dc.date.accessioned 2010-05-19T18:22:19Z
dc.date.available 2010-05-19T18:22:19Z
dc.date.copyright 1995 en
dc.date.issued 2010-05-19T18:22:19Z
dc.identifier.uri http://hdl.handle.net/1828/2782
dc.description.abstract Many earlier works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, summation of series, et cetera). The main object of the present paper is to examine rather systematically (and extensively) some of the most recent contributions on the applications of fractional calculus operators involving power functions and in finding the sums of several interesting families of infinite series. Various other classes of infinite sums found in the mathematical literature by these (or other) means, and their validity or hitherto unnoticed connections with some known results, are also considered. en
dc.description.sponsorship National Science Council of the Republic of China Grant NSC-85-2121-M-001-013 and NSERC Grant OGP0007353 en
dc.language.iso en en
dc.relation.ispartofseries DMS-717-IR en
dc.subject fractional calculus en
dc.subject summation of series en
dc.subject ordinary and partial differential equations en
dc.subject integral equations en
dc.subject differintegral operator en
dc.subject Riemann-Liouville operator en
dc.subject Weyl operator en
dc.subject hypergeometric function en
dc.subject Leibniz rule en
dc.subject Pochhammer symbol en
dc.subject Psi (or Digamma) function en
dc.subject confluent hypergeometric function en
dc.subject hypergeometric sums and transformations en
dc.subject analytic continuation formula en
dc.subject reflection formula en
dc.subject Kummer's summation theorem en
dc.subject power functions en
dc.subject Legendre's duplication formula en
dc.title Fractional calculus operators and their applications involving power functions and summation of series en
dc.type Technical Report en

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