Usman, TalhaNisar, Kottakkaran SooppyBaleanu, DumitruNadeem, Raghib02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2022-03-222025-09-182022-03-222025-09-182020Nadeem, Raghib...et al. (2020). "Analytical properties of the Hurwitz-Lerch zeta function", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://doi.org/10.1186/s13662-020-02924-2https://hdl.handle.net/123456789/10578Usman, Talha/0000-0002-4208-6784; Nisar, Prof. Kottakkaran Sooppy/0000-0001-5769-4320; Nadeem, Raghib/0000-0001-7013-4248In the present paper, we aim to extend the Hurwitz-Lerch zeta function Phi delta,sigma;gamma(xi ,s,upsilon ;p) involving the extension of the beta function (Choi et al. in Honam Math. J. 36(2):357-385, 2014). We also study the basic properties of this extended Hurwitz-Lerch zeta function which comprises various integral formulas, a derivative formula, the Mellin transform, and the generating relation. The fractional kinetic equation for an extended Hurwitz-Lerch zeta function is also obtained from an application point of view. Furthermore, we obtain certain interesting relations in the form of particular cases.eninfo:eu-repo/semantics/openAccessGeneralizedGenerating FunctionsRodrigues Formula33C0533C4533C4733C90Article10.1186/s13662-020-02924-22-s2.0-85090398815