Some stability results on non-linear singular differential systems with random impulsive moments

Arumugam  Vinodkumar; Sivakumar  Harinie; Michal  Fečkan; Jehad Alzabut

doi:10.11121/ijocta.2023.1327

Authors

Arumugam Vinodkumar Department of Mathematics, Amrita School of Physical Sciences, Coimbatore-641 112, Amrita Vishwa Vidyapeetham, India https://orcid.org/0000-0002-5314-8768
Sivakumar Harinie Department of Mathematics, Amrita School of Physical Sciences, Coimbatore-641 112, Amrita Vishwa Vidyapeetham, India https://orcid.org/0009-0003-3172-3869
Michal Fečkan Mathematical Institute, Slovak Academy of Sciences, Stef´anikova 49, 814 73 Bratislava, Slovakia https://orcid.org/0000-0002-7385-6737
Jehad Alzabut Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia https://orcid.org/0000-0002-5262-1138

DOI:

https://doi.org/10.11121/ijocta.2023.1327

Keywords:

Random impulses, Lyapunov function, Exponential stability, Singular differential systems

Abstract

This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoretical results' effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well.

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Author Biographies

Arumugam Vinodkumar, Department of Mathematics, Amrita School of Physical Sciences, Coimbatore-641 112, Amrita Vishwa Vidyapeetham, India

Arumugam Vinodkumar works as an Associate Professor in the Department of Mathematics, School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore Campus. He completed his Ph.D. in Random impulsive Differential Systems and Stochastic Differential Systems. Now he is working on qualitative behaviors of the differential systems. He serves as a reviewer for some prestigious journals and societies.

Sivakumar Harinie, Department of Mathematics, Amrita School of Physical Sciences, Coimbatore-641 112, Amrita Vishwa Vidyapeetham, India

Sivakumar Harinie is currently working as an Amazon and Key Accounts Analyst at Hatley Little Blue House Inc, Montreal, Canada. She completed her Master's Degree, MSc in Mathematics, at the School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore Campus. Additionally, she has completed a Master's Program in Data Analyst and Data Scientist at Simplilearn, Bangalore.

Michal Fečkan, Mathematical Institute, Slovak Academy of Sciences, Stef´anikova 49, 814 73 Bratislava, Slovakia

Michal Fečkan has been a Professor of Mathematics at the Department of Mathematical Analysis and Numerical Mathematics in the Faculty of Mathematics, Physics, and Informatics at Comenius University in Bratislava, Slovakia, since 2003. He received his Master’s degree from Comenius University in Bratislava in 1985 and his Ph.D. from the Mathematical Institute of the Slovak Academy of Sciences in Bratislava, Slovakia, in 1993. He is interested in nonlinear functional analysis, bifurcation theory, dynamical systems, and fractional calculus with applications to mechanics, vibrations, and economics. He is a Highly Cited Researcher in Mathematics.

Jehad Alzabut, Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia

Jehad Alzabut is a professor of Applied Mathematics. He received his Ph.D. degree from Middle East Technical University, Turkey. His area of interest is qualitative properties of delay, difference, fractional, and impulsive differential equations. He has particular interest in mathematical models describing biological and medical phenomena. He serves the role of an editor and a reviewer for some prestigious journals and societies.

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