SOME FURTHER EXTENSIONS CONSIDERING DISCRETE PROPORTIONAL FRACTIONAL OPERATORS

In this paper, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC). To date, discrete fractional systems with complex dynamics have attracted the most consideration. By considering discrete ((h)over bar) PI-proportional fractional operator with nonlocal kernel, this study contributes to the major consequences of the certain novel versions of reverse Minkowski and related Holder-type inequalities via discrete ((h)over bar) PI-proportional fractional sums, as presented. The proposed system has an intriguing feature not investigated in the literature so far, it is characterized by the nabla ((h)over bar) fractional sums. Novel special cases are reported with the intention of assessing the dynamics of the system, as well as to highlighting the several existing outcomes. In terms of applications, we can employ the derived consequences to investigate the existence and uniqueness of fractional difference equations underlying worth problems. Finally, the projected method is efficient in analyzing the complexity of the system.

Automated summary

This paper investigates the dynamic features of discrete fractional calculus (DFC), specifically focusing on discrete fractional systems with complex dynamics. By considering discrete PI-proportional fractional operator, the author derives novel versions of reverse Minkowski and Holder-type inequalities, contributing to major results. The proposed system exhibits an intriguing feature characterized by nabla fractional sums. The author reports novel special cases to assess system dynamics and highlight existing outcomes. The method is efficient in analyzing system complexity and can be applied to investigate the existence and uniqueness of fractional difference equations.