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Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter

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  • Sivashankar, M.
  • Sabarinathan, S.
  • Nisar, Kottakkaran Sooppy
  • Ravichandran, C.
  • Kumar, B.V. Senthil

Abstract

This study is devoted to developing mathematical models associated with the Helmholtz equation as a second-order oscillator involved with nonlinear Caputo fractional difference equations. This study also focuses on determining the approximate solution of this model via the Ulam stability conception. Some properties of the mathematical model dealt with in this study are also presented. Numerical simulations are presented to justify the existence of stability results.

Suggested Citation

  • Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000620
    DOI: 10.1016/j.chaos.2023.113161
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    References listed on IDEAS

    as
    1. El-Dib, Yusry O., 2022. "The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 552-562.
    2. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
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    Cited by:

    1. Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Chenkuan Li, 2023. "On a New Approach for Stability and Controllability Analysis of Functional Equations," Mathematics, MDPI, vol. 11(16), pages 1-35, August.
    2. Gautam, Pooja & Shukla, Anurag, 2023. "Stochastic controllability of semilinear fractional control differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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