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

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dc.contributor.authorChen, M-P.
dc.contributor.authorSrivastava, H.M.
dc.date.accessioned2010-05-19T18:22:19Z
dc.date.available2010-05-19T18:22:19Z
dc.date.copyright1995en
dc.date.issued2010-05-19T18:22:19Z
dc.description.abstractMany 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.sponsorshipNational Science Council of the Republic of China Grant NSC-85-2121-M-001-013 and NSERC Grant OGP0007353en
dc.identifier.urihttp://hdl.handle.net/1828/2782
dc.language.isoenen
dc.relation.ispartofseriesDMS-717-IRen
dc.subjectfractional calculus
dc.subjectsummation of series
dc.subjectordinary and partial differential equations
dc.subjectintegral equations
dc.subjectdifferintegral operator
dc.subjectRiemann-Liouville operator
dc.subjectWeyl operator
dc.subjecthypergeometric function
dc.subjectLeibniz rule
dc.subjectPochhammer symbol
dc.subjectPsi (or Digamma) function
dc.subjectconfluent hypergeometric function
dc.subjecthypergeometric sums and transformations
dc.subjectanalytic continuation formula
dc.subjectreflection formula
dc.subjectKummer's summation theorem
dc.subjectpower functions
dc.subjectLegendre's duplication formula
dc.subjecttechnical reports (mathematics and statistics)
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleFractional calculus operators and their applications involving power functions and summation of seriesen
dc.typeTechnical Reporten

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