In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct computation and obtain the properties of Green function. For \(p(t)\ne \) constant, under the appropriate conditions of the nonlinear term, we establish the existence result of at least one positive solution of the above problem by means of the Leray–Schauder fixed point theorem. Meanwhile, we also obtain the positive extremal solutions and iterative schemes in view of applying a monotone iterative method. For \(p(t)=\) constant, by using Guo–Krasnoselskii fixed point theorem, we study the existence of positive solutions of the above problem. These results enrich the ones in the existing literatures. Finally, some examples are included to demonstrate our main results in this paper and we give out an open problem.

在本文中，我们研究了带有p（t）-Laplacian算子的混合分数阶积分边值问题。首先，我们通过直接计算导出格林函数，并获得格林函数的性质。对于\（p（t）\ ne \）常数，在非线性项的适当条件下，我们通过Leray-Schauder不动点定理建立了上述问题的至少一个正解的存在结果。同时，针对单调迭代法，我们也得到了极值解和迭代方案。对于\（p（t）= \）常数，通过使用Guo–Krasnoselskii不动点定理，我们研究了上述问题的正解的存在。这些结果丰富了现有文献中的结果。最后，包括一些示例以证明本文的主要结果，并提出一个未解决的问题。