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Some miscellaneous properties and applications of certain operators of fractional calculus. (English) Zbl 1223.26009
From the abstract: The main object of this paper is to consider some miscellaneous properties and applications which are associated with several fractional differintegral operators. We investigate, in a systematic and unified manner, various families of series identities which emerged in connection with some fractional differintegral formulas. By using such operators of fractional calculus, a number of integral formulas as well as fractional differintegral formulas involving inverse hyperbolic functions are also evaluated.
MSC:
26A33Fractional derivatives and integrals (real functions)
33B15Gamma, beta and polygamma functions
33C05Classical hypergeometric functions, 2 F 1
33C20Generalized hypergeometric series, p F q
33C60Hypergeometric integrals and functions defined by them