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Some Recent Developments On Dynamical „ -Discrete Fractional Type Inequalities In The Frame Of Nonsingular And Nonlocal Kernels

Author

Listed:
  • 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)

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.

Suggested Citation

  • Saima Rashid & Elbaz I. Abouelmagd & Aasma Khalid & Fozia Bashir Farooq & Yu-Ming Chu, 2022. "Some Recent Developments On Dynamical „ -Discrete Fractional Type Inequalities In The Frame Of Nonsingular And Nonlocal Kernels," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-15, March.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:02:n:s0218348x22401107
    DOI: 10.1142/S0218348X22401107
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    Cited by:

    1. Kang, Daekook & Devi, S. Aicevarya & Felix, Augustin & Narayanamoorthy, Samayan & Kalaiselvan, Samayan & Balaenu, Dumitru & Ahmadian, Ali, 2022. "Intuitionistic fuzzy MAUT-BW Delphi method for medication service robot selection during COVID-19," Operations Research Perspectives, Elsevier, vol. 9(C).

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