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

Saima Rashid (), Elbaz I. Abouelmagd (), Aasma Khalid (), Fozia Bashir Farooq () and Yu-Ming Chu
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Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Elbaz I. Abouelmagd: Celestial Mechanics and Space Dynamics Research Group, Astronomy Department National Research, Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
Aasma Khalid: Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan
Fozia Bashir Farooq: Imam Mohammad Ibn Saud Islamic University, Riyadh, KSA, Saudi Arabia
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China6Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 02, 1-15

Abstract: Discrete fractional calculus (𠒟ℱ𠒞) 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 (𠒜ℬ)-fractional operator having ℠-discrete generalized Mittag-Leffler kernels in the sense of Riemann type (𠒜ℬℛ). Certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete 𠒜ℬ-fractional operators having ℠-discrete generalized Mittag-Leffler kernels are given. Moreover, several other generalizations can be generated for nabla ℠-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.

Keywords: Discrete Fractional Calculus; â„ -Discrete Mittag-Leffler Function; Minkowski Inequality; Nabla â„ -Fractional Sums (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401107

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