On The Problem for A Mixed-Type Degenerate Equation with Caputo and Erdélyi–Kober Operators of Fractional Order

Abstract

We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolichyperbolic-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)) is contained in the Erdelyi–Kober integrals and the hyperbolic equation is degenerated in the line 𝓎 = 0, the existence and uniqueness of solution of the investigated problem are proved by using the properties of hypergeometric functions, the estimates for these functions, and certain integral equalities.