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Extended Riemann-Liouville fractional derivative operator and its applications. (English) Zbl 1329.26010

Summary: Many authors have introduced and investigated certain extended fractional derivative operators. The main object of this paper is to give an extension of the Riemann-Liouville fractional derivative operator with the extended Beta function given by H. M. Srivastava, P. Agarwal and S. Jain [“Generating functions for the generalized Gauss hypergeometric functions”, Appl. Math. Comput. 247, 348–352 (2014; doi:10.1016/j.amc.2014.08.105)] and investigate its various (potentially) useful and (presumably) new properties and formulas, for example, integral representations, Mellin transforms, generating functions, and the extended fractional derivative formulas for some familiar functions.

MSC:

26A33 Fractional derivatives and integrals
33C05 Classical hypergeometric functions, \({}_2F_1\)
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C65 Appell, Horn and Lauricella functions
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