A Cauchy-Goursat problem for a second kind degenerated equation of hyperbolic type

Abstract

In the work a Cauchy-Goursta problem has been formulated and investigated for a second kind degenerated equation of hyperbolic type. During the investigation, it was used properties of Gauss’s hyper geometric function and symbol of Pochhammer, the considered problem equivalently reduced to an integral equation with respect to trace of unknown function. Properties of Riemann-Liuvill integral-differential and generalized integral-differential operators have found solution of the taken integral equation. To find solution of the problem it was used general solution of the equation. A class of generalized solutions was introduced for the correctness of the problem. It was found necessary conditions for the given functions