Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic Type Equation with Caputo and Erdelyi–Kober Operators of Fractional Order

Abstract

The work is devoted to the proof of the uniqueness and existence of solution to local and nonlocal problems with an integral gluing condition for a loaded parabolic-hyperbolic type equation with differential and integral operators of fractional order, in which the trace of the solution appears in the Erdelyi–Kober integral operator. Using the method of energy integrals, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations.