We consider the well-known classes of functions $\mathcal{U}_{1}(\mathbf{v},\mathtt{k})$ and $\mathcal{U}_{2}(\mathbf{v},\mathtt{k})$, and those of Opial inequalities defined on these classes. In view of these indices, we establish new aspects of the Opial integral inequality and related inequalities, in the context of fractional integrals and derivatives defined using nonsingular kernels, particularly the Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) models of fractional calculus.

中文翻译：

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具有非奇异核的广义分数算子的Opial积分不等式

我们考虑函数$ \ mathcal {U} _ {1}（\ mathbf {v}，\ mathtt {k}）$和$ \ mathcal {U} _ {2}（\ mathbf {v} ，\ mathtt {k}）$，以及在这些类上定义的Opial不等式。鉴于这些指标，我们在使用非奇异核定义的分数积分和导数的背景下，建立了Opial积分不等式和相关不等式的新方面，尤其是分数的Caputo-Fabrizio（CF）和Atangana-Baleanu（AB）模型结石。