najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-4-418-424najo-456Research ArticleMATHEMATICSМАТЕМАТИКАAnalog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivativeАналог задачи Дарбу для нагруженного интегро-дифференциального уравнения с дробной производной КапутоBaltaevaU.BaltaevaU.

Markaz-1, 220900, Khiva;

Kh.Alimdjan str. 14, 220100, Urgench.

Markaz-1, 220900, Khiva;

Kh.Alimdjan str. 14, 220100, Urgench.

umida_baltayeva@mail.ruAlikulovY.AlikulovY.

Amir Temur str. 108, 100200 Tashkent.

Amir Temur str. 108, 100200 Tashkent.

yolqin-aliqulov@mail.ruBaltaevaI. I.BaltaevaI. I.

Kh.Alimdjan str. 14, 220100, Urgench.

Kh.Alimdjan str. 14, 220100, Urgench.

iroda-b@mail.ruAshirovaA.AshirovaA.

Al Khorezmi str. 110, 220100 Urgench.

Al Khorezmi str. 110, 220100 Urgench.

Khorezm Mamun Academy; Urgench State UniversityKhorezm Mamun Academy; Urgench State UniversityTashkent University of Information Technologies named after Muhammad Al-KhwarizmiTashkent University of Information Technologies named after Muhammad Al-KhwarizmiUrgench State UniversityUrgench State UniversityUrganch branch of Tashkent University of Information Technology named after Muhammad al-KhwarizmiUrganch branch of Tashkent University of Information Technology named after Muhammad al-Khwarizmi202104082025124418424Copyright © Baltaeva U., Alikulov Y., Baltaeva I.I., Ashirova A., 20252025Baltaeva U., Alikulov Y., Baltaeva I.I., Ashirova A.Baltaeva U., Alikulov Y., Baltaeva I.I., Ashirova A.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/456

In this paper, we prove the unique solvability of an analogue problem Darboux for a loaded integro-differential equation with Caputo operator by method of integral equations. The problem is equivalently reduced to a system of integral equations, which is unconditionally and uniquely solvable.

В данной работе методом интегральных уравнений доказана однозначная разрешимость аналога задачи Дарбу для нагруженного интегро-дифференциального уравнения с оператором Капуто. Задача равносильно сводится к системе интегральных уравнений, безусловно и однозначно разрешимой.

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