U. Baltaeva, Y. Alikulov, I. I. Baltaeva, A. Ashirova, “Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative”, Nanosystems: Physics, Chemistry, Mathematics, 2021, Volume 12, Issue 4,Pages <nobr>418

This article is cited in 7 papers

MATHEMATICS

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

U. Baltaeva^ab, Y. Alikulov^c, I. I. Baltaeva^b, A. Ashirova^d

^a Khorezm Mamun Academy, Markaz-1, 220900, Khiva, Uzbekistan
^b Urgench State University, Kh.Alimdjan str. 14, 220100, Urgench, Uzbekistan
^c Tashkent University of Information Technologies named after Muhammad Al-Khwarizmi, Amir Temur str. 108, 100200 Tashkent, Uzbekistan
^d Urganch branch of Tashkent University of Information Technology named after Muhammad al-Khwarizmi, Al Khorezmi str. 110, 220100 Urgench, Uzbekistan

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.

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

Received: 09.06.2021
Revised: 17.07.2021

Language: English

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