Boundary value problems for a mixed-type loaded equation with a characteristic and noncharacteristic line of type change

Abstract

In this work, we consider boundary value problems with characteristic, non-characteristic, and two mixed lines of type change for a fractionally loaded equation. The equation under consideration is a loaded parabolic-hyperbolic type with a fractional integral operator, where the hyperbolic part is a characteristic load. By assuming the load is characteristic under necessary conditions on the given functions, we prove the unique solvability of the resulting integral equations derived from the formulated problems. Consequently, the problems also have unique solutions.