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

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1009 Downloads
• 2080 Views

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.

Share and Cite

Keywords

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

MSC

•  34A08
•  34E10
•  34E15

References

• [1] V. P. Dyakonov, Maple 7. Training course, Peter, St. Petersburg (2003)
  • Google Scholar


• [2] B. T. Kalimbetov, On the question of asymptotic integration of singularly perturbed fractional order problems, Asian J. Fuzzy Appl. Math., 6 (2018), 44--49
  • View Article
  • Google Scholar


• [3] B. T. Kalimbetov, Regularized asymptotics of solutions for systems of singularly perturbed differential equations of fractional order, Int. J. Fuzzy Math. Arch., 16 (2018), 67--74
  • View Article
  • Google Scholar


• [4] B. T. Kalimbetov, Scalar singularly perturbed Cauchy problem for a differential equation of fractional order, Asian J. Fuzzy Appl. Math., 7 (2019), 10--13
  • View Article
  • Google Scholar


• [5] B. T. Kalimbetov, V. F. Safonov, A regularization method for systems with unstable spectral value of the kernel of the integral operator, J. Differ. Equ., 31 (1995), 647--656
  • Google Scholar


• [6] B. T. Kalimbetov, M. A. Temirbekov, Z. O. Khabibullayev, Asymptotic solutions of singular perturbed problems with an instable spectrum of the limiting operator, Abstr. Appl. Anal., 2012 (2012), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [7] U. N. Katugampola, Correction to "What is a fractional derivative?" by Ortigueira and Machado, J. Comput. Phys., 321 (2016), 1255--1257
  • View Article
  • Google Scholar


• [8] R. Khalil, M. Al Horani, D. Anderson, Undetermined coefficients for local fractional differential equations, J. Math. Comput. Sci., 16 (2016), 140--146
  • View Article
  • Google Scholar


• [9] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Comput. Appl. Math., 264 (2014), 65--70
  • View Article
  • Google Scholar


• [10] M. N. Kirsanov, Graphs in Maple, Fizmatlit, Moscow (2007)
  • Google Scholar


• [11] S. A. Lomov, Introduction to General Theory of Singular Perturbations, American Mathematical Society, Providence (1992)
  • View Article
  • MathSciNet
  • Google Scholar