Numerical solutions to the fractional-order wave equation

M. M. Khader, Mustafa Inc, M. Adel and M. Ali Akinlar ()
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M. M. Khader: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia2Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Mustafa Inc: Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey4Department of Medical Research, China Medical University, Taichung, Taiwan
M. Adel: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia6Department of Mathematics, Faculty of Science Cairo University, Giza, Egypt
M. Ali Akinlar: Engineering Sciences Department, Faculty of Engineering and Natural Sciences, Bandirma Onyedi Eylul University, 10200 Bandirma, Balikesir, Turkey

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 05, 1-10

Abstract: New numerical solution to the linear fractional-order wave equation is presented. The Liouville–Caputo sense fractional-derivative operator and Crank–Nicholson finite difference method (CN-FDM) algorithm are employed. The stability of the present technique is considered by the fractional Von Neumann stability analysis method. Special example as an application of the method is provided. The obtained results are examined to check the derived stability condition of the proposed algorithm. Computational results indicate that the present numerical algorithm is efficient and applicable for the problem under study and many other problems.

Keywords: Fractional-order wave equation; Von Neumann type stability; Crank–Nicholson method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500675

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