We study the Cauchy problem for a degenerate differential equation of beam vibrations. Using the generalized Erdélyi–Kober operator, possessing the property of a transmutation operator, we reduce the original problem to a problem for a nondegenerate equation. An explicit formula for the solution is constructed.
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Dedicated to the outstanding mathematician Makhmud Salakhitdinovich Salakhitdinov on the occasion of his 90th anniversary
International Mathematical Schools. Vol. 6. Mathematical Schools in Uzbekistan
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Sitnik, S., Karimov, S. & Tulasheva, Y. The Cauchy Problem for the Degenerate Beam Vibration Equation. J Math Sci 277, 458–466 (2023). https://doi.org/10.1007/s10958-023-06849-5
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DOI: https://doi.org/10.1007/s10958-023-06849-5