Some generating relations for extended hypergeometric functions via generalized fractional derivative operator

Recently various extensions of Hurwitz-Lerch Zeta functions have been investigated. Here, we first introduce a further generalization of the extended Hurwitz-Lerch Zeta functions. Then we investigate certain interesting and (potentially) useful properties, systematically, of the generalization of the extended Hurwitz-Lerch Zeta functions, for example, various integral representations, Mellin transform, generating functions and extended fractional derivatives formulas associated with these extended generalized Hurwitz-Lerch Zeta functions. An application to probability distributions is further considered. Some interesting special cases of our main results are also pointed out.

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“…In recent years, some extensions of the well-known special functions have been considered by several authors (see, for example, [4,8,9,11,15,16,[18][19][20]31]). The familiar incomplete gamma functions γ (s, x) and (s, …”

Section: Introductionmentioning

confidence: 99%

Incomplete Caputo fractional derivative operators

Özarslan

Ustaoğlu

2018

Adv Differ Equ

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The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral representations. Furthermore, we define incomplete Caputo fractional derivative operators and show that the images of some elementary functions under the action of incomplete Caputo fractional operators give a new type of incomplete hypergeometric functions. This definition helps us to obtain linear and bilinear generating relations for the new type incomplete Gauss hypergeometric functions.

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Some generating relations for extended hypergeometric functions via generalized fractional derivative operator

Cited by 63 publications

References 7 publications

Extension of the fractional derivative operator of the Riemann-Liouville

Extension of the fractional derivative operator of the Riemann-Liouville

Further generalization of the extended Hurwitz-Lerch Zeta functions

Incomplete Caputo fractional derivative operators

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