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Article

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

by
Mathiyalagan Kalidass
1,*,
Shengda Zeng
2,* and
Mehmet Yavuz
3
1
Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
2
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China
3
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya 42090, Türkiye
*
Authors to whom correspondence should be addressed.
Axioms 2022, 11(7), 308; https://doi.org/10.3390/axioms11070308
Submission received: 27 May 2022 / Revised: 10 June 2022 / Accepted: 17 June 2022 / Published: 25 June 2022
(This article belongs to the Special Issue Nonlinear Dynamical Systems with Applications)
Review Reports Versions Notes

Abstract

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.
Keywords: fractional-order system; quasi-linear system; impulse; integro-differential equation; stability; multiple delays fractional-order system; quasi-linear system; impulse; integro-differential equation; stability; multiple delays

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MDPI and ACS Style

Kalidass, M.; Zeng, S.; Yavuz, M. Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays. Axioms 2022, 11, 308. https://doi.org/10.3390/axioms11070308

AMA Style

Kalidass M, Zeng S, Yavuz M. Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays. Axioms. 2022; 11(7):308. https://doi.org/10.3390/axioms11070308

Chicago/Turabian Style

Kalidass, Mathiyalagan, Shengda Zeng, and Mehmet Yavuz. 2022. "Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays" Axioms 11, no. 7: 308. https://doi.org/10.3390/axioms11070308

APA Style

Kalidass, M., Zeng, S., & Yavuz, M. (2022). Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays. Axioms, 11(7), 308. https://doi.org/10.3390/axioms11070308

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