In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane \(\mathbb{R} ^{2}\). Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

中文翻译：

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关于通过广义分数积分的协调凸函数的广义 Ostrowski、Simpson 和梯形类型不等式

在这项研究中，我们证明了涉及双重广义分数积分和一些参数的二次部分可微映射的恒等式。通过使用这个已建立的恒等式，我们为平面\(\mathbb{R} ^{2}\) 中具有矩形的可微协调凸函数提供了一些广义不等式。此外，通过在我们的主要结果中特殊选择参数，我们获得了几个众所周知的不等式，例如 Ostrowski 不等式、梯形不等式以及 Riemann 和 Riemann-Liouville 分数积分的 Simpson 不等式。