In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications, an example is offered to illustrate our main results.

中文翻译：

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非线性脉冲分数阶微分系统正解的存在唯一性及最优控制

本文研究了一种涉及控制项的脉冲分数阶微分系统。通过使用一类φ-凹-混合混合单调算子不动点定理，得到关于脉冲分数阶微分方程正解存在性和唯一性的定理，并研究了正解的最优控制问题。作为应用程序，提供了一个示例来说明我们的主要结果。