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REVIEW ARTICLE

A comprehensive review on fractional-order coronavirus models: Optimization of numerical results, control, applications, and future predictions

Kottakkaran Sooppy Nisar1* ,  Muhammad Farman2,3 ,  Khadija Jamil4 ,  Muhammad Kamran5
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1 Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia
2 Department of Mathematics, Mathematics Research Center, Near East University, North Nicosia, Northern Cyprus, Turkey
3 Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan
4 International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore, Punjab, Pakistan
5 Research Institute of Business Analytics and SCM, College of Management, Shenzhen University, Shenzhen, Guangdong, China
IJOCTA, 026060022 https://doi.org/10.36922/IJOCTA026060022
Received: 3 February 2026 | Revised: 14 March 2026 | Accepted: 18 March 2026 | Published online: 14 May 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 outbreak of the COVID-19 pandemic has highlighted the need for advanced mathematical tools capable of accurately describing complex disease transmission dynamics. Fractional calculus has emerged as a powerful modeling framework due to its ability to incorporate memory effects and nonlocal behavior, which are intrinsic to infectious disease spread. This review provides a comparison of solutions obtained through the application of various fractional operators, including Caputo, Caputo–Fabrizio, Atangana–Baleanu derivative in Caputo sense, and fractal-fractional derivatives with power-law, exponential decay, and Mittag–Leffler memories. Key analytical properties such as positivity, boundedness, equilibrium analysis, basic reproduction number estimation, existence and uniqueness of solutions, Hyers–Ulam–Rassias stability, and chaos control are systematically discussed. The review further highlights the application of fractional models in capturing the effects of vaccination, quarantine, hospitalization, environmental transmission, and control interventions. By consolidating recent theoretical and applied advances, this work demonstrates the superiority of fractional-order models over classical integer-order approaches in reproducing real world COVID-19 dynamics. The presented review serves as a valuable reference for researchers and policymakers seeking robust and flexible modeling strategies for epidemic analysis and control.

Keywords
COVID-19 model
Caputo fractional derivative
Hyers–Ulam–Rassias stability
Chaos
Numerical optimization control
Funding
This work is funded by Prince Sattam bin Abdulaziz University, project number (PSAU/2025/RV/12).
Conflict of interest
The authors declare they have 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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