Baleanu, DumitruNadeem, RaghibUsman, TalhaNisar, Kottakkaran SooppyBaleanu, Dumitru2022-03-222022-03-222020Nadeem, Raghib...et al. (2020). "Analytical properties of the Hurwitz-Lerch zeta function", Advances in Difference Equations, Vol. 2020, No. 1.1687-1839https://hdl.handle.net/20.500.12416/5153In 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 FormulaArticle2020110.1186/s13662-020-02924-2