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Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative

https://doi.org/10.17586/2220-8054-2021-12-4-418-424

Abstract

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.

About the Authors

U. Baltaeva
Khorezm Mamun Academy; Urgench State University
Uzbekistan

Markaz-1, 220900, Khiva;

Kh.Alimdjan str. 14, 220100, Urgench.



Y. Alikulov
Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi
Uzbekistan

Amir Temur str. 108, 100200 Tashkent.



I. I. Baltaeva
Urgench State University
Uzbekistan

Kh.Alimdjan str. 14, 220100, Urgench.



A. Ashirova
Urganch branch of Tashkent University of Information Technology named after Muhammad al-Khwarizmi
Uzbekistan

Al Khorezmi str. 110, 220100 Urgench.



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Review

For citations:


Baltaeva U., Alikulov Y., Baltaeva I.I., Ashirova A. Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative. Nanosystems: Physics, Chemistry, Mathematics. 2021;12(4):418-424. https://doi.org/10.17586/2220-8054-2021-12-4-418-424

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)