In this paper, without requiring the complete continuity of integral operators and the existence of upper–lower solutions, by means of the sum-type mixed monotone operator fixed point theorem based on the cone $P_{h}$, we investigate a kind of p-Laplacian differential equation Riemann–Stieltjes integral boundary value problem involving a tempered fractional derivative. Not only the existence and uniqueness of positive solutions are obtained, but also we can construct successively sequences for approximating the unique positive solution. As an application of our fundamental aims, we offer a realistic example to illustrate the effectiveness and practicability of the main results.

中文翻译：

---

带p -Laplacian算子的非线性回火分数阶微分方程正解的存在唯一性和单调迭代

本文在不需要积分算子的完全连续性和上下解的存在的情况下，借助于基于圆锥$ P_ {h} $的和型混合单调算子不动点定理，研究了一种p-Laplacian微分方程Riemann–Stieltjes积分边值问题，涉及回火的分数导数。不仅获得了正解的存在性和唯一性，而且我们可以连续构造近似唯一解的序列。作为我们基本目标的应用，我们提供了一个现实的例子来说明主要结果的有效性和实用性。