A boundary problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative

Abstract

In the present work we investigate the Tricomi problem with an integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional differential operator. Using the method of energy integrals, we prove the uniqueness of the solution for the considered problem. The existence of the solution have been proved applying methods of ordinary differential equations and Fredholm integral equations. The solution is represented in an explicit form.

Keywords

• Parabolic-hyperbolic equation
• Tricomi problem
• Caputo fractional derivative
• Green's function