In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers–Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo–Krasnoselskii’s fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.

在本文中，我们处理具有涉及p-Laplacian算子的不同阶分数导数的一般非线性分数阶微分方程（FDE）正解的存在性和唯一性。我们还研究了溶液的Hyers-Ulam（HU）稳定性。对于存在的结果，我们使用格林函数建立FDE的积分形式，然后通过应用Guo–Krasnoselskii不动点定理获得解的存在性。为了我们的目的，我们还检查了Green函数的属性。结果的唯一性是通过应用Banach收缩映射原理建立的。提供了一个示例，以确保我们的结果的有效性。