On the problem for the mixed-type degenerate equation with Caputo and Erdelyi – Kober operators of fractional order

Abstract

UDC 517.9
We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolic-hyperbolic-type equations with loaded terms containing the trace of solution in the Erdelyi – Kober integrals. Since, the trace of solution (i.e., $u(x, 0)$) appears in the Erdelyi – Kober integrals and the hyperbolic-type equation is degenerated in the line $y = 0$, we use some properties and estimates for hypergeometric functions and, in addition, some integral equalities in proving the existence and uniqueness of solution of the investigated problem.