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

In this paper, the method of transmutation operators is used to construct an exact solution Goursat problem for a fourth-order hyperbolic equation with singular Bessel operator. We emphasise that in many other papers and monographs fractional Erdélyi-Kober are as integral operators, but our approach them additional new properties important applications. Specifically, it extends its applications differential equations, especially Bessel-type operators. Using operator, under consideration reduced similar without The resulting auxiliary solved by Riemann method. On basis, original constructed analyzed.