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Solution of the Goursat Problem for a Fourth-Order Hyperbolic Equation with Singular Coefficients by the Method of Transmutation Operators

Author

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  • Sergei M. Sitnik

    (Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy Street, 85, 308015 Belgorod, Russia)

  • Shakhobiddin T. Karimov

    (Department of Applied Mathematics and Informatics, Fergana State University (FSU), Murabbiylar Street, 3A, Fergana 150100, Uzbekistan)

Abstract

In this paper, the method of transmutation operators is used to construct an exact solution of the Goursat problem for a fourth-order hyperbolic equation with a singular Bessel operator. We emphasise that in many other papers and monographs the fractional Erdélyi-Kober operators are used as integral operators, but our approach used them as transmutation operators with additional new properties and important applications. Specifically, it extends its properties and applications to singular differential equations, especially with Bessel-type operators. Using this operator, the problem under consideration is reduced to a similar problem without the Bessel operator. The resulting auxiliary problem is solved by the Riemann method. On this basis, an exact solution of the original problem is constructed and analyzed.

Suggested Citation

  • Sergei M. Sitnik & Shakhobiddin T. Karimov, 2023. "Solution of the Goursat Problem for a Fourth-Order Hyperbolic Equation with Singular Coefficients by the Method of Transmutation Operators," Mathematics, MDPI, vol. 11(4), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:951-:d:1066731
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    Cited by:

    1. Shakhobiddin Karimov & Yorkinoy Tulasheva, 2024. "Solution of an Initial Boundary Value Problem for a Multidimensional Fourth-Order Equation Containing the Bessel Operator," Mathematics, MDPI, vol. 12(16), pages 1-11, August.
    2. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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