On the asymptotic solutions of singulary perturbed differential systems of fractional order

Volume 24, Issue 2, pp 165--172 http://dx.doi.org/10.22436/jmcs.024.02.07

Publication Date: February 14, 2021 Submission Date: February 20, 2020 Revision Date: December 13, 2020 Accteptance Date: January 01, 2021

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Authors

Burkhan Kalimbetov - Khoja Ahmet Yasawi International Kazakh-Turkish University, B. Sattarkhanov 29, Turkestan, Kazakhstan. Elmyra Abylkasymova - University of Friendship of People's Academican A. Kuatbekov, Toleby 32, Shymkent, Kazakhstan. Gulbakhram Beissenova - University of Friendship of People's Academican A. Kuatbekov, Toleby 32, Shymkent, Kazakhstan. - M. Auezov South Kazakhstan University, Take-Khan avenue 7, Shymkent, Kazakhstann.

Abstract

In this paper, we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. A regularization problem is produced, and an algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of the small parameter are constructed.

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Keywords

• Matrix-function
• vector-function
• differential equation of fractional order
• regularization
• asymptotic
• iterative problems
• normal and unique solvability

MSC

•  34A08
•  34E10
•  34E15

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