BOUNDARY-VALUE PROBLEMS WITH GENERALIZED GLUING CONDITIONS FOR A LOADED DIFFERENTIAL EQUATION WITH A PARABOLIC-HYPERBOLIC OPERATOR

In the present work we study the unique solvability of local boundary value problems with generalized gluing conditions for the third order differential equation with a loaded parabolic-hyperbolic operator

Extension of the Tricomi problem for a loaded parabolic–hyperbolic equation with a characteristic line of change of type

In this work, we investigate a generalization of the Tricomi problem for a loaded mixed-type equation with the Riemann–Liouville fractional differential operator. By using the method of integral equations, a unique solvability of the formulated problem given in piecewise non-parallel characteristics is proven. © 2022 John Wiley & Sons, Ltd

Cauchy problem for a parabolic–hyperbolic equation with non-characteristic line of type changing

In this work, we present the advanced fractional model described with the loaded parabolic–hyperbolic-type equation. Also, for this equation, we investigate a Cauchy-type problem with a line of changing type. The existence and uniqueness of the solutions to the problem are proven using the theory of integral equations. © 2022 John Wiley & Sons, Ltd