Unique Solution of an Infinite 2-System Model of First Order Ordinary Differential Equation

Authors

  • Idham Arif Alias Department of Mathematics and Statistics, Universiti Putra Malaysia, Serdang, Selangor
  • Muhammad Arif Syazani Mohd Yazid Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor
  • Gafurjan Ibragimov V.I.Romanovskiy Institute of Mathematics Academy of Sciences of Uzbekistan 100174, Tashkent

Abstract

This work is to solve an infinite 2-system model of first order ordinary differential equations. The system is in Hilbert space l2 with the coefficients are any positive real numbers. The system is rewritten as a system in the form of matrix equations and it is first studied in R2 where its solution is obtained and a fundamental matrix is constructed. The results are carried out to solve the infinite 2-system in Hilbert space l2 . The control functions satisfy integral constraint and are elements of the space of square integrable function in l2 . The existence and uniqueness of the solution of the system in Hilbert space l2 on an interval time [0, T] for a sufficiently large T is then proven.

Keywords:

Infinite 2-system, Hilbert space, matrix, differential equation

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Published

2023-04-10

How to Cite

Idham Arif Alias, Muhammad Arif Syazani Mohd Yazid, & Gafurjan Ibragimov. (2023). Unique Solution of an Infinite 2-System Model of First Order Ordinary Differential Equation. Applied Mathematics and Computational Intelligence (AMCI), 12(1), 87–100. Retrieved from https://ejournal.unimap.edu.my/index.php/amci/article/view/208

Issue

Vol. 12 No. 1 (2023): April (2023)

Section

Articles