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

Yimiao Zhang, Muhammad Idrees Afridi (), Muhammad Samad Khan and Amanullah
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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

Mathematics, 2025, vol. 13, issue 3, 1-17

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.

Keywords: wavelet; Hermite polynomial; HWM method; Bagley–Torvik equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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