MATHEMATICAL AND STABILITY ANALYSIS OF FRACTIONAL ORDER MODEL FOR SPREAD OF PESTS IN TEA PLANTS

Zain Ul Abadin Zafar, Zahir Shah, Nigar Ali, Ebraheem O. Alzahrani and Meshal Shutaywi
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Zain Ul Abadin Zafar: Faculty of Information Technology, University of Central Punjab, Lahore, Pakistan
Zahir Shah: ��Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
Nigar Ali: ��Department of Mathematics, University of Malakand, Pakistan
Ebraheem O. Alzahrani: �Department of Mathematics, Faculty of Science, King Abdulaziz, University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Meshal Shutaywi: �Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-14

Abstract: In this paper, the fractional order model for the binge of pests in tea plants is studied numerically. This model consists of three compartments such as tea plant, pest and predator. The local and non-local stability investigation of the system is also deliberated. The Grunwald–Letnikov (GL coefficients) method and generalized Euler method (GEM) are used to elucidate and simulate the proposed system. We have obtained stability conditions for equilibrium points, provided a numerical example, and proved our results. The results illustrate the concentrations of tea plants, pests, and predators all reach their equilibrium values as time passes. An imperative feature of this model is that it controls the motion at which the solution to equilibrium is grasped.

Keywords: Numerical Method; Fractional Order; Stability Analysis; The Natural Enemy; Generalized Euler Method; GL Coefficients (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500080

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