On a non-local boundary problem for a parabolic-hyperbolic equation involving a Riemann-Liouville fractional differential operator (Q765261)

A nonlocal boundary value problem with special gluing conditions for a mixed parabolic-hyperbolic equation with parameter is introduced and studied. The parabolic part of this equation is a fractional analogue of heat equation and the hyperbolic part is the telegraph equation. The considered problem is reduced, for positive values of the parameter, to an equivalent system of the second kind Volterra integral equations. By use of the Green functions and the properties of integro-differential operators, the authors show the existence and uniqueness of solutions of the formulated problem in a specific function space.