We establish a coincidence point theorem in complete metric spaces. As a consequence, we show the existence of solutions to a system of initial value problem of fractional differential equations involving Riemann–Liouville fractional derivatives. Next, we derive several coincidence point theorems for new classes of sublinear and superlinear operators, in the context of ordered Banach spaces. Finally, we apply these results to discuss the existence of positive solutions to a class of initial value problem of fractional differential equations.

中文翻译：

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重合点定理及其在分数阶微分方程中的应用

我们在完整的度量空间中建立一个重合点定理。结果，我们证明了涉及Riemann-Liouville分数阶导数的分数阶微分方程初值问题系统的解的存在。接下来，在有序Banach空间的背景下，我们推导了一些新的亚线性和超线性算子类的重合点定理。最后，我们将这些结果用于讨论一类分数阶微分方程初值问题的正解的存在。