Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order

This work devoted to uniqueness and existence of solution of the local and non-local problems with integral gluing condition for the loaded parabolic-hyperbolic type equation involving Caputo derivatives which trace of solution involved into the Erdelyi-Kober integral operator. The uniqueness of solution is proved using by the method of integral energy. The existence of solution was proved by the method of integral equations.