AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA026370262
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RESEARCH ARTICLE

Stability analysis and optimal control theory for a class of plant disease models under a fractional derivative

Ndolane Sene1* ,  Karima Abdelmalek2
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1 Department of Mathematics of Decision, Cheikh Anta Diop University, Dakar , Senegal
2 Department of Mathematics, Faculty of Science and Technology, University of Souk Ahras, Souk Ahras , Algeria
IJOCTA, 026370262 https://doi.org/10.36922/IJOCTA026370262
Received: 9 September 2026 | Revised: 28 October 2026 | Accepted: 2 November 2026 | Published online: 13 November 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The present paper focuses on plant disease modeling using the Caputo derivative. To ensure that the problem is biologically well defined, we establish the non-negativity and boundedness of the solutions of the dynamical system. The stability of the equilibrium points is analyzed in detail. A two-stage fractionalorder Runge-Kutta method is considered within the fractional-calculus framework for the present model and is adopted in this paper. A computational algorithm for the fractional second-order Runge-Kutta method is proposed. We conclude this investigation by proposing two control strategies to facilitate eradication of the plant disease under consideration.

Keywords
Caputo derivative
Runge Kutta method
Stability analysis
Optimal control
Fractional calculus
Funding
None.
Conflict of interest
The author declares there are no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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