In this paper, we prove that F iterative scheme is almost stable for weak contractions. Further, we prove convergence results for weak contractions as well as for generalized non-expansive mappings due to Hardy and Rogers via F iterative scheme. We also prove that F iterative scheme converges faster than the some known iterative schemes for weak contractions. An illuminative numerical example is formulated to support our assertion. Finally, utilizing our main result the solution of nonlinear fractional differential equation is approximated.

中文翻译：

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F迭代格式的稳定性和收敛性及其在分数阶微分方程中的应用

在本文中，我们证明了 F 迭代方案对于弱收缩几乎是稳定的。此外，我们通过 F 迭代方案证明了由于 Hardy 和 Rogers 导致的弱收缩以及广义非膨胀映射的收敛结果。我们还证明了 F 迭代方案比一些已知的弱收缩迭代方案收敛得更快。制定了一个说明性的数值例子来支持我们的断言。最后，利用我们的主要结果近似非线性分数阶微分方程的解。