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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
Version 1
: Received: 19 June 2024 / Approved: 19 June 2024 / Online: 19 June 2024 (15:02:19 CEST)
How to cite:
Karimov, S.; Tulasheva, Y. 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. Preprints2024, 2024061363. https://doi.org/10.20944/preprints202406.1363.v1
Karimov, S.; Tulasheva, Y. 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. Preprints 2024, 2024061363. https://doi.org/10.20944/preprints202406.1363.v1
Karimov, S.; Tulasheva, Y. 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. Preprints2024, 2024061363. https://doi.org/10.20944/preprints202406.1363.v1
APA Style
Karimov, S., & Tulasheva, Y. (2024). 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. Preprints. https://doi.org/10.20944/preprints202406.1363.v1
Chicago/Turabian Style
Karimov, S. and Yorkinoy Tulasheva. 2024 "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" Preprints. https://doi.org/10.20944/preprints202406.1363.v1
Abstract
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.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
