NEW DEVELOPMENTS IN WEIGHTED n-FOLD TYPE INEQUALITIES VIA DISCRETE GENERALIZED (h)over-cap-PROPORTIONAL FRACTIONAL OPERATORS

This study explores some significant consequences of discrete (h) over cap -proportional fractional sums (D (h) over cap PFs) having an exponential function as a nonlocal kernel. Certain novel weighted versions comprising a group of positive mappings via (D (h) over cap PFs) are given. A variety of refinements can be derived by taking into account the extraction of the new estimates and the nabla (h) over cap -fractional sums. The suggested technique is a revolutionary formulation of conventional operators that may be used to design efficient mechanism descriptions in short time spans by provoking certain noteworthy properties of chaos theory. Moreover, novel generalizations of the discrete h-fractional sum can be generated by the specific value of the proportionality index. Derived outcomes and investigation confirm that the proposed plan will offer gains in many modeling and chaotic framework applications.

Automated summary

This study explores the significant consequences of discrete (h) over cap proportional fractional sums (D (h) over cap PFs) with an exponential function as a nonlocal kernel. It suggests a revolutionary technique for designing efficient mechanism descriptions based on chaos theory. Various refinements and generalizations of the discrete h-fractional sum can be derived, offering potential gains in modeling and chaotic framework applications.