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On the Oscillation of Non-Linear Fractional Difference Equations with Damping

Author

Listed:
  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Velu Muthulakshmi

    (Department of Mathematics, Periyar University, Salem 636 011, India)

  • Abdullah Özbekler

    (Department of Mathematics, Atilim University, Ankara 06830, Turkey)

  • Hakan Adıgüzel

    (Department of Architecture and Urban Planning, Vocational School of Arifiye, Sakarya University of Applied Sciences, Arifiye 54580, Turkey)

Abstract

In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.

Suggested Citation

  • Jehad Alzabut & Velu Muthulakshmi & Abdullah Özbekler & Hakan Adıgüzel, 2019. "On the Oscillation of Non-Linear Fractional Difference Equations with Damping," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:687-:d:253751
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    References listed on IDEAS

    as
    1. Chunxia Qi & Junmo Cheng, 2013. "Interval Oscillation Criteria for a Class of Fractional Differential Equations with Damping Term," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, April.
    2. Zhihong Bai & Run Xu, 2018. "The Asymptotic Behavior of Solutions for a Class of Nonlinear Fractional Difference Equations with Damping Term," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-11, January.
    3. Tongbo Liu & Bin Zheng & Fanwei Meng, 2013. "Oscillation on a Class of Differential Equations of Fractional Order," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-13, September.
    4. Bin Zheng & Qinghua Feng, 2013. "Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    Full references (including those not matched with items on IDEAS)

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