NON-LOCAL PROBLEM FOR A LOADED PARABOLIC-HYPERBOLIC EQUATION INVOLVING CAPUTO AND ERDELYI-KOBER OPERATORS

This research work devoted to the formulation and the study of non-local boundary value problem with integral gluing condition for the loaded parabolic-hyperbolic equation with Caputo fractional derivatives. Loaded terms of a considering equation are Erdelyi-Kober integrals, which involves a trace of solution on the line of changing type (i.e. u(x; 0)). Formulated problem is investigates, considering to cases related with the coe±cients of a non-local condition. Unique solvability of the investigated problem, is proved reducing to the second kind Volterra type integral equations