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 coefficients of a non-local condition.Unique solvability of the investigated problem, is proved reducing to the second kind Volterra type integral equations.

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