A NUMERICAL ANALYSIS OF NABLA DISCRETE OPERATOR: TO INVESTIGATE PREY–PREDATOR MODEL

Aziz Khan (), Hisham Mohammad Alkhawar (), Thabet Abdeljawad and Fehmi Mabrouk ()
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Aziz Khan: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
Hisham Mohammad Alkhawar: ��Preparatory Year Program, Computer Department, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia‡Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India§Department of Medical Research, China Medical University, Taichung 40402, Taiwan¶Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, 02447 Seoul, Korea∥Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa
Fehmi Mabrouk: University of Gafsa, Higher Institute of Applied Sciences and Technology of Gafsa, Tunisia

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-12

Abstract: In this paper, we propose a fractional-order nabla difference nonlinear system involving bounded disturbances and utilizing the numerical analysis to investigate the prey–predator model in the sense of the nabla difference operator. This system class has a broader range of nonlinearities in comparison to the Lipschitz class. We develop adequate criteria for the observer design based on the one-sided Lipschitz and quadratically inner-bounded ones. We prove the practical Mittag-Leffler stability of the closed-loop system. Furthermore, we provided a separation principle for a class of nonlinear systems with bounded uncertain parts. We illustrated a numerical example to show the efficacy and application of our new findings.

Keywords: Nabla Difference Operator; Discrete Mittag-Leffler; Stability; Lyapunov Analysis; Numerical Analysis; Fractional Order; Output Feedback Stabilization; Separation Principle (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401115

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