In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

中文翻译：

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关于具有两个变量的有界变分函数的一些新的分数阶 Ostrowski 型和梯形型不等式

在本文中，我们首先证明了有界变化函数的三个恒等式。然后，通过使用这些等式，我们通过具有两个变量的有界变化函数的广义分数积分获得几个梯形和 Ostrowski 型不等式。此外，我们通过对主要结果的特殊选择，给出了黎曼-刘维尔分数阶积分的一些结果。最后，我们调查了我们的结果与早期作品之间的联系。这种性质的分析不等式，尤其是所涉及的技术，在对称性发挥突出作用的各个领域都有应用。