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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.
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