SOME RECENT DEVELOPMENTS ON DYNAMICAL ℏ-DISCRETE FRACTIONAL TYPE INEQUALITIES IN THE FRAME OF NONSINGULAR AND NONLOCAL KERNELS

Abstract

Discrete fractional calculus ([Formula: see text]) is significant for neural networks, complex dynamic systems and frequency response analysis approaches. In contrast with the continuous-time frameworks, fewer outcomes are accessible for discrete fractional operators. This study investigates some major consequences of two sorts of inequalities by considering discrete Atangana–Baleanu [Formula: see text]-fractional operator having [Formula: see text]-discrete generalized Mittag-Leffler kernels in the sense of Riemann type ([Formula: see text]). Certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-fractional operators having [Formula: see text]-discrete generalized Mittag-Leffler kernels are given. Moreover, several other generalizations can be generated for nabla [Formula: see text]-fractional sums. The proposing discretization is a novel form of the existing operators that can be provoked by some intriguing features of chaotic systems to design efficient dynamics description in short time domains. Furthermore, by combining two mechanisms, numerous new special cases are introduced.