Geodesic
Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 33-46

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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.
Keywords: loaded equation, parabolic-hyperbolic type, Caputo derivatives, integral gluing condition, uniqueness and existence of solution, integral equations. 
@article{IVM_2020_10_a3,
     author = {B. I. Islomov and O. Kh. Abdullaev},
     title = {Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with {Caputo} and {Erdelyi-Kober} operators of fractional order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--46},
     publisher = {mathdoc},
     number = {10},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_10_a3/}
}
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%A O. Kh. Abdullaev
%T Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 33-46
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%F IVM_2020_10_a3
B. I. Islomov; O. Kh. Abdullaev. Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 33-46. http://geodesic.mathdoc.fr/item/IVM_2020_10_a3/