https://doi.org/10.1140/epjs/s11734-024-01437-3
Regular Article
A fractional-order optimal control models for plant-locust surveillance mechanism with singular and non-singular derivative operators
1
Department of Mathematics, Alagappa University, 630 004, Karaikudi, India
2
Department of Mathematics, Central University of Tamil Nadu, 610 005, Thiruvarur, India
3
Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138, Mersin 10, Turkey
4
Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, 02841, Seoul, South Korea
5
Department of Technical Sciences, Western Caspian University, 1001, Baku, Azerbaijan
Received:
28
March
2024
Accepted:
14
November
2024
Published online:
7
January
2025
We introduce a fractional-order mathematical model to study plant growth with locust control using neem oil and locust fertilizer. This model employs singular and nonsingular derivatives, including Caputo, Caputo–Fabrizio (CF), and Atangana–Baleanu Caputo (ABC) derivatives. We analyze the uniqueness and stability of the model and propose an optimal control strategy that involves a cost-effective, time-dependent application of neem oil to enhance crop production and mitigate locust populations over a given time period. We derive the necessary and sufficient conditions for optimal control. Numerical simulations, using two-step Lagrange interpolation polynomial methods for forward simulations and Runge–Kutta methods for backward simulations, demonstrate that the optimal control significantly reduces the gregarious locust population, facilitating their transition to a solitarious state due to neem oil application. Furthermore, the results suggest that the CF derivative outperforms the Caputo and ABC derivatives in boosting crop production during locust infestations.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
