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

Ahmed M. Elshenhab; Xingtao Wang; Fatemah Mofarreh; Omar Bazighifan

doi:10.32604/cmes.2022.021512

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

Ahmed M. Elshenhab^*
, Xingtao Wang
, Fatemah Mofarreh
, Omar Bazighifan^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
Mansoura University
Princess Nourah Bint Abdulrahman University
International Telematic University Uninettuno

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 delayedmatrix 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.

Original language	English
Pages (from-to)	927-940
Number of pages	14
Journal	CMES - Computer Modeling in Engineering and Sciences
Volume	134
Issue number	2
DOIs	https://doi.org/10.32604/cmes.2022.021512
State	Published - 2023
Externally published	Yes

Keywords

Representation of solutions
conformable delayed matrix function
conformable fractional delay differential equations
conformable fractional derivative
finite time stability

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10.32604/cmes.2022.021512

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title = "Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay",

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 delayedmatrix 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.",

keywords = "Representation of solutions, conformable delayed matrix function, conformable fractional delay differential equations, conformable fractional derivative, finite time stability",

author = "Elshenhab, \{Ahmed M.\} and Xingtao Wang and Fatemah Mofarreh and Omar Bazighifan",

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TY - JOUR

T1 - Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

AU - Elshenhab, Ahmed M.

AU - Wang, Xingtao

AU - Mofarreh, Fatemah

AU - Bazighifan, Omar

PY - 2023

Y1 - 2023

N2 - 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 delayedmatrix 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.

AB - 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 delayedmatrix 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.

KW - Representation of solutions

KW - conformable delayed matrix function

KW - conformable fractional delay differential equations

KW - conformable fractional derivative

KW - finite time stability

UR - https://www.scopus.com/pages/publications/85138824760

U2 - 10.32604/cmes.2022.021512

DO - 10.32604/cmes.2022.021512

M3 - 文章

AN - SCOPUS:85138824760

SN - 1526-1492

VL - 134

SP - 927

EP - 940

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

IS - 2

ER -

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

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Keywords

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