On a certain extension of the Riemann-Liouville fractional derivative operator. (English) Zbl 1426.33016
Summary: The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by M. Shadab, S. Jabee and J. Choi [“An extension of beta function and its application”, Far East J. Math. Sci. (FJMS) 103, No. 1, 235–251 (2018)]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell’s function via generating functions.
MSC:
| 33C15 | Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) |
| 26A33 | Fractional derivatives and integrals |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C65 | Appell, Horn and Lauricella functions |
Keywords:
hypergeometric function; beta function; extended hypergeometric function; Mellin transform; fractional derivative; Appell’s functionSoftware:
DLMFReferences:
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