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In the present work we investigate the Tricomi problem with integral gluingcondition for parabolic-hyperbolic equation with the Caputo fractional orderderivative. Using the method of energy integrals we prove the uniqueness of thesolution for considered problem. The existence will be proved using methods ofordinary differential equations, Fredholm integral equations and solution willbe represented in an explicit form.

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