najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-3-323-333najo-604Research ArticleMATHEMATICSМАТЕМАТИКАOn a problem for the loaded degenerating mixed type equation involving integral-differential operatorsIslomovB. I.

Universitetskaya-4, VUZgorodog, Tashkent, 100174

islomovbozor@yandex.ruAbdullayevO. Kh.

Universitetskaya-4, VUZgorodog, Tashkent, 100174

obidjon.mth@gmail.comOchilovaN. K.

st. Amir Timur. 57, Tashkent, 100000

nargiz.ochilova@gmail.comNational University of UzbekistanUzbekistanTashkent financial instituteUzbekistan20171108202583323333Copyright © Islomov B.I., Abdullayev O.K., Ochilova N.K., 20252025Islomov B.I., Abdullayev O.K., Ochilova N.K.Islomov B.I., Abdullayev O.K., Ochilova N.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/604

This work aims to study the existence and uniqueness of a solution for a problem of the loaded degenerating mixed type equation. We consider the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals. The uniqueness of solution is proved by using the method of integral energy applying an extremum principle. Based on the statement of equivalence between “The existence and uniqueness of solution” and “Solvability of the respectively Fredholm type integral equations”, the existence of a solution was proved.

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The authors declare that there are no conflicts of interest present.