Uniform asymptotic stability of \(q\)-deformed conformable fractional systems with delay and application

Volume 30, Issue 1, pp 38--47 https://doi.org/10.22436/jmcs.030.01.05

Publication Date: November 25, 2022 Submission Date: July 21, 2022 Revision Date: August 12, 2022 Accteptance Date: September 09, 2022

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Authors

N. Kamsrisuk - Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand. P. Srisilp - Rail System Institute of Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand. T. Botmart - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand. J. Tariboon - Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand. J. Piyawatthanachot - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand. W. Chartbupapan - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand. K. Mukdasai - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand.

Abstract

In this article, we initiate the study of new concepts of conformable \(q\)-fractional calculus. The conformable fractional \(q\)-derivative and \(q\)-integral are defined and their fundamental theorems are also proved. The uniform asymptotic stability of the \(q\)-deformed conformable fractional system with constant delay is investigated by using the Lyapunov-Razumikhin method. For application, a new asymptotic stability necessary condition for the conformable \(q\)-fractional linear system with constant delay is obtained in term of linear matrix inequality (LMI). A numerical example is demonstrated for the results given to illustrate the effectiveness.

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Keywords

• \(q\)-deformed conformable fractional system
• Lyapunov-Razumikhin theorem
• uniform asymptotic stability
• linear matrix inequality

MSC

•  34K20
•  34K25
•  34K37

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