IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1356-d796840.html
   My bibliography  Save this article

Neutral Differential Equations of Second-Order: Iterative Monotonic Properties

Author

Listed:
  • Osama Moaaz

    (Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Fahd Masood

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, Faculty of Science, Sana’a University, Sana’a 12544, Yemen
    Department of Mathematics, Faculty of Education and Science, University of Sheba Region, Sheba Region 16822, Yemen)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

  • Shami A. M. Alsallami

    (Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • E. M. Khalil

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohamed L. Bouazizi

    (Department of Mechanical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Alkharj 16273, Saudi Arabia)

Abstract

In this work, we investigate the oscillatory properties of the neutral differential equation ( r ( l ) [ ( s ( l ) + p ( l ) s ( g ( l ) ) ) ′ ] v ) ′ + ∑ i = 1 n q i ( l ) s v ( h i ( l ) ) = 0 , where s ≥ s 0 . We first present new monotonic properties for the solutions of this equation, and these properties are characterized by an iterative nature. Using these new properties, we obtain new oscillation conditions that guarantee that all solutions are oscillate. Our results are a complement and extension to the relevant results in the literature. We test the significance of the results by applying them to special cases of the studied equation.

Suggested Citation

  • Osama Moaaz & Fahd Masood & Clemente Cesarano & Shami A. M. Alsallami & E. M. Khalil & Mohamed L. Bouazizi, 2022. "Neutral Differential Equations of Second-Order: Iterative Monotonic Properties," Mathematics, MDPI, vol. 10(9), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1356-:d:796840
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1356/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/9/1356/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Osama Moaaz & Dimplekumar Chalishajar & Omar Bazighifan, 2019. "Some Qualitative Behavior of Solutions of General Class of Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-12, July.
    3. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Osama Moaaz & Mona Anis & Dumitru Baleanu & Ali Muhib, 2020. "More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    5. Agarwal, Ravi P. & Zhang, Chenghui & Li, Tongxing, 2016. "Some remarks on oscillation of second order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 178-181.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Osama Moaaz & Rami Ahmad El-Nabulsi & Ali Muhib & Sayed K. Elagan & Mohammed Zakarya, 2021. "New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    2. Osama Moaaz & Yousef Alnafisah, 2023. "An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    3. Osama Moaaz & Clemente Cesarano, 2021. "New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    4. Bazighifan, Omar, 2020. "On the oscillation of certain fourth-order differential equations with p-Laplacian like operator," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Osama Moaaz & Mona Anis & Dumitru Baleanu & Ali Muhib, 2020. "More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    6. Omar Bazighifan & Ioannis Dassios, 2020. "Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    7. Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    8. Akgül, Ali & Partohaghighi, Mohammad, 2022. "New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    11. Omar Bazighifan & Clemente Cesarano, 2019. "Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    12. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    13. Shahram Rezapour & Sina Etemad & Ravi P. Agarwal & Kamsing Nonlaopon, 2022. "On a Lyapunov-Type Inequality for Control of a ψ -Model Thermostat and the Existence of Its Solutions," Mathematics, MDPI, vol. 10(21), pages 1-11, October.
    14. Nasibeh Mollahasani, 2024. "A Hybrid Spectral-Finite Difference Method for Numerical Pricing of Time-Fractional Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 841-869, August.
    15. Marappan Sathish Kumar & Omar Bazighifan & Alanoud Almutairi & Dimplekumar N. Chalishajar, 2021. "Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms," Mathematics, MDPI, vol. 9(9), pages 1-9, April.
    16. Osama Moaaz & Jan Awrejcewicz & Ali Muhib, 2020. "Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    17. Muhammad Aamir Ali & Fongchan Wannalookkhee & Hüseyin Budak & Sina Etemad & Shahram Rezapour, 2022. "New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
    18. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    19. Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
    20. Asma Al-Jaser & Belgees Qaraad & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior," Mathematics, MDPI, vol. 11(12), pages 1-15, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1356-:d:796840. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.