The aim of this paper is to evaluate the potential improvement of classification results in the frame of discrete proportional fractional operator. The nonlocal kernel of the generalized proportional fractional sum depending on $\widehat{h}$-discrete exponential functions defined on time scale $\widehat{h}\mathbb{Z}$. This paper deals novel discrete versions of the Pólya-Szegö and ČebyšeV type inequalities via discrete $\widehat{h}$-proportional fractional sums. These generalizations have potential utilities in the study of finite difference equations and statistical analysis. Taking into account the discrete $\widehat{h}$-proportional fractional sums, the main consequences concerns a quite general form of the Pólya-Szegö and ČebyšeV variants. In addition, the present investigation is a discrete analogue of integral inequalities established in the relative literature and also expands several discrete variants for nabla $\widehat{h}$-fractional sums in particular.

本文的目的是评估离散比例分数算子框架中分类结果的潜在改进。广义比例分数和的非局部核取决于$\widehat{H}$在时标上定义的离散指数函数 $\widehat{H}\mathbb{ž}$。本文通过离散处理Pólya-Szegö和ČebyšeV型不等式的新颖离散形式$\widehat{H}$比例小数和。这些概括在有限差分方程的研究和统计分析中具有潜在的实用性。考虑到离散$\widehat{H}$-小数和的比例，主要后果涉及Pólya-Szegö和ČebyšeV变体的相当普通的形式。此外，本研究是在相关文献中建立的积分不等式的离散模拟，并且扩展了nabla的多个离散变体。$\widehat{H}$-小数总和。