ABSTRACT In this article, we discuss the existence and uniqueness of solutions to a class of integral boundary value problem of fractional differential equations. Different fractional order derivations are included in the nonlinear term and boundary conditions. The unique solution is derived by a new fixed point theorem of increasing -concave operators defined on ordered sets. Further, we construct a monotone iterative scheme to approximate the unique solution. An example is given to illustrate the validity of our main results.

中文翻译：

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涉及积分边界条件的分数阶微分方程的解

摘要 在本文中，我们讨论了一类分数阶微分方程积分边值问题解的存在唯一性。非线性项和边界条件中包含不同的分数阶导数。唯一的解决方案是由在有序集合上定义的递增-凹算子的新不动点定理推导出来的。此外，我们构造了一个单调迭代方案来逼近唯一解。给出了一个例子来说明我们主要结果的有效性。