In the present paper, we aim to extend the Hurwitz–Lerch zeta function \(\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)\) 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.

在本文中，我们旨在扩展Hurwitz–Lerch zeta函数\（\ varPhi _ {\ delta，\ varsigma; \ gamma}（\ xi，s，\ upsilon; p）\），涉及beta函数的扩展（Choi等人在Honam Math。J. 36（2）：357-385，2014中）。我们还研究了扩展的Hurwitz-Lerch zeta函数的基本属性，该函数包含各种积分公式，导数公式，Mellin变换和生成关系。还可以从应用的角度获得扩展的Hurwitz-Lerch zeta函数的分数动力学方程。此外，我们以特定案例的形式获得了某些有趣的关系。