The main goal of this paper is estimating certain new fractional integral inequalities for the extended Chebyshev functional in the sense of synchronous functions by employing proportional fractional integral (PFI) and Hadamard proportional fractional integral. We establish certain inequalities concerning one- and two-parameter proportional and Hadamard proportional fractional integrals. We also discuss certain particular cases.

中文翻译：

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某些新的比例和Hadamard比例分数积分不等式

本文的主要目的是通过使用比例分数积分（PFI）和Hadamard比例分数积分，在同步函数的意义上估计扩展的Chebyshev泛函的某些新的分数积分不等式。我们建立了关于一参量和二参量比例积分和Hadamard比例分数积分的某些不等式。我们还将讨论某些特定情况。