Obtaining a representation of the solution of the Cauchy problem for one equation with a fractional derivative and applying it to the equation of forced beam vibrations

摘要

In the article, a representation of the solution of a Cauchy‐type problem for a high‐order equation with a fractional Hilfer derivative is obtained. The uniqueness of the solution of the stated problem is shown. The obtained solutions are applied to obtain a unique solution of the Cauchy problem for the equation of forced vibrations of the beam.