In this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness of a positive solution and the Hyers–Ulam-type stability. To proceed this work, we utilize the tools of fixed point theory and nonlinear analysis to investigate the concern theory. We convert fractional differential equation into an integral alternative form with the help of the Greens function. Using the desired function, we studied the existence of a positive solution and uniqueness for proposed class of fractional differential equation. In next section of this work, the author presents stability analysis for considered problem and developed the conditions for Ulam’s type stabilities. Furthermore, we also provided two examples to illustrate our main work.

在本文中，我们研究一类非线性分数阶微分方程，它关于一个正解的存在和唯一性以及Hyers-Ulam型稳定性。为了进行这项工作，我们利用定点理论和非线性分析的工具来研究关注理论。我们借助格林函数将分数阶微分方程转换为积分替代形式。使用期望的函数，我们研究了拟议的分数阶微分方程的正解的存在性和唯一性。在本工作的下一部分中，作者将对所考虑的问题进行稳定性分析，并为Ulam的类型稳定性建立条件。此外，我们还提供了两个示例来说明我们的主要工作。