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Investigating an Approximate Solution for a Fractional-Order Bagley–Torvik Equation by Applying the Hermite Wavelet Method

Author

Listed:
  • Yimiao Zhang

    (Research Center for Mathematical Modeling and Simulation, Hanjiang Normal University, Shiyan 442000, China)

  • Muhammad Idrees Afridi

    (Research Center for Mathematical Modeling and Simulation, Hanjiang Normal University, Shiyan 442000, China)

  • Muhammad Samad Khan

    (Department of Mathematics, NED University of Engineering and Technology, University Road, Karachi 75270, Pakistan)

  • Amanullah

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

Abstract

In this paper, we introduce the Hermite wavelet method (HWM), a numerical method for the fractional-order Bagley–Torvik equation (BTE) solution. The recommended method is based on a polynomial called the Hermite polynomial. This method uses collocation points to turn the given differential equation into an algebraic equation system. We can find the values of the unknown constants after solving the system of equations using the Maple program. The required approximation of the answer was obtained by entering the numerical values of the unknown constants. The approximate solution for the given fractional-order differential equation is also shown graphically and numerically. The suggested method yields straightforward results that closely match the precise solution. The proposed methodology is computationally efficient and produces more accurate findings than earlier numerical approaches.

Suggested Citation

  • Yimiao Zhang & Muhammad Idrees Afridi & Muhammad Samad Khan & Amanullah, 2025. "Investigating an Approximate Solution for a Fractional-Order Bagley–Torvik Equation by Applying the Hermite Wavelet Method," Mathematics, MDPI, vol. 13(3), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:528-:d:1584273
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    References listed on IDEAS

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    1. Bhalekar, Sachin & Gade, Prashant M. & Joshi, Divya, 2022. "Stability and dynamics of complex order fractional difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Yihang Zeng & Zhengchao Xia & Kaifei Kang & Jiacheng Zhu & Patrick Knüppel & Chirag Vaswani & Kenji Watanabe & Takashi Taniguchi & Kin Fai Mak & Jie Shan, 2023. "Thermodynamic evidence of fractional Chern insulator in moiré MoTe2," Nature, Nature, vol. 622(7981), pages 69-73, October.
    3. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
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