A unifying computational framework for novel estimates involving discrete fractional calculus approaches

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 ĥ-discrete exponential functions defined on time scale ĥZ. This paper deals novel discrete versions of the Pólya-Szegö and ČebyšeV type inequalities via discrete ĥ-proportional fractional sums. These generalizations have potential utilities in the study of finite difference equations and statistical analysis. Taking into account the discrete ĥ-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 ĥ-fractional sums in particular.