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

Sergei M. Sitnik () and Shakhobiddin T. Karimov
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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

Mathematics, 2023, vol. 11, issue 4, 1-9

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.

Keywords: Goursat problem; Bessel operator; transmutation operator; Erdélyi-Kober operator; Riemann method; fourth-order equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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