Solution of the Cauchy problem for a hyperbolic equation of the fourth order with the Bessel operator by the method of transmutation operators

Karimov, Sh. T.; Oripov, Shukrullo

doi:10.1007/s40590-023-00496-1

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…Note that in the works [20][21][22][23][24] the Erdélyi-Kober operators were used as a transmutation operator when solving initial and boundary value problems for hyperbolic type equations with the Bessel operator, and in the works [18,19,25] they were used for parabolic type equations with the Bessel operator.…”

Section: Multidimensional Erdélyi-kober Transmutation Operatormentioning

confidence: 99%

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Application of the Transmutation Operator Method to the Solution of an Initial Boundary Value Problem for the Equation of Multidimensional Free Transverse Vibration of a Thin Elastic Plate Containing the Bessel Operator

Karimov,

Tulasheva

2024

Preprint

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In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

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