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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2021, 12 (4), P. 418–424

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

U. Baltaeva – Khorezm Mamun Academy, Markaz-1, 220900, Khiva; Urgench State University, Kh.Alimdjan str. 14, 220100, Urgench, Uzbekistan; umida_baltayeva@mail.ru
Y. Alikulov – Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi, Amir Temur str. 108, 100200 Tashkent, Uzbekistan; yolqin-aliqulov@mail.ru
I. I. Baltaeva – Urgench State University, Kh.Alimdjan str. 14, 220100, Urgench, Uzbekistan; iroda-b@mail.ru
A. Ashirova – Urganch branch of Tashkent University of Information Technology named after Muhammad al-Khwarizmi, Al Khorezmi str. 110, 220100 Urgench, Uzbekistan; anorgul@mail.ru

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.

Keywords: integro-differential equations, Caputo fractional derivative, loaded equation, nonlocal problem, Bessel function.

PACS 02.30.Jr

DOI 10.17586/2220-8054-2021-12-4-418-424

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