Open Access

ARTICLE

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

Ahmed M. Elshenhab^1,2,*, Xingtao Wang¹, Fatemah Mofarreh³, Omar Bazighifan^4,*

1 School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
3 Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh, 11546, Saudi Arabia
4 Section of Mathematics, International Telematic University Uninettuno, Roma, 00186, Italy

* Corresponding Authors: Ahmed M. Elshenhab. Email: ; Omar Bazighifan. Email:

(This article belongs to the Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 134(2), 927-940. https://doi.org/10.32604/cmes.2022.021512

Received 18 January 2022; Accepted 23 March 2022; Issue published 31 August 2022

Abstract

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results.

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Keywords

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