In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

中文翻译：

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Caputo多项式半线性微分方程的分数构型正解的分析

在本文中，我们考虑涉及 Caputo 分数阶导数的多项半线性分数边值问题，并通过不同给定条件的项研究正解的存在性。为此，我们首先研究格林函数的性质，然后通过定义两个下控制函数和上控制函数，并使用众所周知的 Schauder 不动点定理，我们得到所需的存在标准。在论文的最后，我们基于给定的边值问题给出了一个数值例子，并得到了它的上下解，最后，我们将这些正解与精确解进行了图形比较。