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New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations

Author

Listed:
  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Qingkai Kong

    (Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA)

  • Rami Ahmad El-Nabulsi

    (Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand
    Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Waranont Anukool

    (Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand
    Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of a 2 ( ζ ) φ α 2 a 1 ζ φ α 1 x Δ ( ζ ) Δ Δ + q ( ζ ) φ α x ( g ( ζ ) ) = 0 , on a time scale T , where Δ is the forward operator on T , α 1 , α 2 , α > 0 , and g , q , a i , i = 1 , 2 , are positive r d -continuous functions on T , and φ θ ( u ) : = u θ − 1 u . Our results in this paper are new and substantial for dynamic equations of the third order on arbitrary time scales. An example is included to illustrate the results.

Suggested Citation

  • Taher S. Hassan & Qingkai Kong & Rami Ahmad El-Nabulsi & Waranont Anukool, 2022. "New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4143-:d:964741
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    References listed on IDEAS

    as
    1. Osama Moaaz & Ioannis Dassios & Omar Bazighifan, 2020. "Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Naveed Iqbal & Humaira Yasmin & Ali Rezaiguia & Jeevan Kafle & A. Othman Almatroud & Taher S. Hassan & Fairouz Tchier, 2021. "Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, December.
    3. Taher S. Hassan & Yuangong Sun & Amir Abdel Menaem, 2020. "Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order," Mathematics, MDPI, vol. 8(11), pages 1-19, October.
    4. Osama Moaaz & Rami Ahmad El-Nabulsi & Waad Muhsin & Omar Bazighifan, 2020. "Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    5. Zhang, Hai & Cheng, Jingshun & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2021. "Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Karpuz, Başak, 2019. "Hille–Nehari theorems for dynamic equations with a time scale independent critical constant," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 336-351.
    7. Taher S. Hassan & Rabie A. Ramadan & Zainab Alsheekhhussain & Ahmed Y. Khedr & Amir Abdel Menaem & Ismoil Odinaev, 2022. "Improved Hille Oscillation Criteria for Nonlinear Functional Dynamic Equations of Third-Order," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    8. Taher S. Hassan & E. M. Elabbasy & A.E. Matouk & Rabie A. Ramadan & Alanazi T. Abdulrahman & Ismoil Odinaev & Binxiang Dai, 2022. "Routh–Hurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-15, April.
    9. Akın, Elvan & Hassan, Taher S., 2015. "Comparison criteria for third order functional dynamic equations with mixed nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 169-185.
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