[
[1] Agrawal O. P., Formulation of euler–lagrange equations for fractional variational problems, Journal of Mathematical Analysis and Applications 272 (1) (2002) 368–379. 435.10.1016/S0022-247X(02)00180-4
]Search in Google Scholar
[
[2] Ahmed E., El-Sayed A., El-Saka H. A., Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models J Math Anal Appl, 325 (1) (2007), pp. 542-553.10.1016/j.jmaa.2006.01.087
]Search in Google Scholar
[
[3] Alqahtani R. T., Yusuf A., and Agarwal R. P., (2021). Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative. Mathematics, 9(6), 675.10.3390/math9060675
]Search in Google Scholar
[
[4] Baleanu D., and Agarwal R. P., (2021). Fractional calculus in the sky. Advances in Difference Equations, 2021(1), 1-9.10.1186/s13662-021-03270-7
]Search in Google Scholar
[
[5] Baleanu D., Mohammadi H., and Rezapour S., (2020). Analysis of the model of HIV-1 infection of CD4+ CD4+ T-cell with a new approach of fractional derivative. Advances in Difference Equations, 2020(1), 1-17. pages.10.1186/s13662-020-02544-w
]Search in Google Scholar
[
[6] Bani-Yaghoub M., Gautam R., Shuai Z., van den Driessche P., and R. Ivanek, Reproduction numbers for infections with free-living pathogens growing in the environment,” Journal of Biological Dynamics, vol. 6, no. 2, pp. 923940, 2012.10.1080/17513758.2012.693206
]Search in Google Scholar
[
[7] Barongo M. B., Bishop R. P., Fèvre E.M., Knobel D. L., and Ssematimba A., (2016). A mathematical model that simulates control options for African swine fever virus (ASFV). PloS one, 11(7), e0158658.10.1371/journal.pone.0158658493863127391689
]Search in Google Scholar
[
[8] Beltrán-Alcrudo D., Arias M., Gallardo C., Kramer S., and Penrith M. L., 2017. African swine fever: detection and diagnosis – A manual for veterinarians. FAO Animal Production and Health Manual No. 19. Rome. Food and Agriculture Organization of the United Nations (FAO). 88
]Search in Google Scholar
[
[9] Birkhoff G. and Rota G. c., Ordinary Differential Equations, 4th edition, JohnWiley & Sons, New York, (1989)
]Search in Google Scholar
[
[10] Bjornstad O. N., Shea K., Krzywinski M., et al. The SEIRS model for infectious disease dynamics. Nat Methods 17, 557–558 (2020). https://doi.org/10.1038/s41592-020-0856-2.10.1038/s41592-020-0856-232499633
]Search in Google Scholar
[
[11] Boyce W. E., DiPrima R. C., Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, New York, (2009).
]Search in Google Scholar
[
[12] Bonyah E., Khan M. A., Okosun K. O., Gomez-Aguilar J. F.,: Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea with optimal control. Math. Biosci. 309, 1/11 (2019)10.1016/j.mbs.2018.12.01530597155
]Search in Google Scholar
[
[13] Driessche P. V.and Watmough J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp.2948, 2002.10.1016/S0025-5564(02)00108-612387915
]Search in Google Scholar
[
[14] Fleming W. H. and Rishel R. W., Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975.10.1007/978-1-4612-6380-7
]Search in Google Scholar
[
[15] Gumel A., Shivakumar P., Sahai B., A mathematical model for the dynamics of HIV-1 during the typical course of infection. Nonlinear Anal 2001;47(3):17731783.10.1016/S0362-546X(01)00309-1
]Search in Google Scholar
[
[16] Halasa T., Botner A., Mortensen S., Christensen H., Wulff S. B., and Boklund A., (2018). Modeling the effects of Duration and size of the control Zones on the consequences of a hypothetical african swine Fever epidemic in Denmark. Frontiers in veterinary science, 5, 49.10.3389/fvets.2018.00049586830229616228
]Search in Google Scholar
[
[17] Kada D., Kouidere A., Balatif O., Rachik M., and Labriji E.H, 2020. Mathematical modeling of the spread of COVID-19 among different age groups in Morocco: Optimal control approach for intervention strategies. Chaos, Solitons and Fractals, p.110437.10.1016/j.chaos.2020.110437783705633519111
]Search in Google Scholar
[
[18] Karrakchou J., Rachik M., S. Gourari. Optimal control and infectiology: application to an HIV/AIDS model. Appl Math Comput 2006;177(2):807818.10.1016/j.amc.2005.11.092
]Search in Google Scholar
[
[19] Khajji B., Kada D., Balatif O., Rachik M., A multi-region discrete time mathematical modeling of the dynamics of Covid-19 virus propagation using optimal control. J. Appl. Math. Comput. (2020). https://doi.org/10.1007/s12190-020-01354-3.10.1007/s12190-020-01354-3720592032390786
]Search in Google Scholar
[
[20] Khan M. A., Shah S. W., Ullah S., Gomez-Aguilar J. F.: A dynamical model of asymptomatic carrier zika virus with optimal control strategies. Nonlinear Anal. Real World Appl. 50, 144/170 (2019)10.1016/j.nonrwa.2019.04.006
]Search in Google Scholar
[
[21] Khan M. A., Atangana A. Modeling the dynamics of novel coronavirus (2019-nCoV) with fractional derivative Alexandria Eng J, 599 (4) (2020), pp. 2379-2389, 10.1016/j.aej.2020.02.03310.1016/j.aej.2020.02.033
]Search in Google Scholar
[
[22] Kim H. J., Cho K. H., Lee S. K., Kim D. Y., ah J. J., et al (2020). Outbreak of African swine fever in South Korea, 2019. Transboundary and emerging diseases, 67(2), 473-475.10.1111/tbed.1348331955520
]Search in Google Scholar
[
[23] Kouidere A., Labzai A., Khajji B., Ferjouchia H., Balatif O., Boutayeb A., Rachik M., Optimal control strategy with multi-delay in state and control variables of a discrete mathematical modeling for the dynamics of diabetic population, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 14 https://doi.org/10.28919/cmbn/4486 ISSN: 2052-2541.10.28919/cmbn/4486
]Search in Google Scholar
[
[24] Kouidere A., Khajji B., El Bhih A., Balatif O., Rachik M., A mathematical modeling with optimal control strategy of transmission of COVID-19 pandemic virus, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 24 https://doi.org/10.28919/cmbn/4599 ISSN: 2052-254110.28919/cmbn/4599
]Search in Google Scholar
[
[25] Kouidere A., Balatif O., Ferjouchia H., Boutayeb A., Rachik M., Optimal Control Strategy for a Discrete Time to the Dynamics of a Population of Diabetics with Highlighting the Impact of Living Environment (2019), Discrete Dynamics in Nature and Society, Article ID 5949303.10.1155/2019/6342169
]Search in Google Scholar
[
[26] Kouidere A., Balatif O., and Rachik M., (2021). Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness. Chaos, Solitons and Fractals, 146, 110867.10.1016/j.chaos.2021.110867
]Search in Google Scholar
[
[27] Kouidere A., Kada D., Balatif O., Rachik M and Naim M., (2020). Optimal Control Approach of a Mathematical Modeling with Multiple Delays of The Negative Impact of Delays in Applying Preventive Precautions against the Spread of the COVID-19 pandemic with a case study of Brazil and Cost-effectiveness. Chaos, Solitons and Fractals, 110438.10.1016/j.chaos.2020.110438
]Search in Google Scholar
[
[28] LaSalle J. P.,”the stability of dynamical systems,” Regional Conference Series in Applied Mathematics, Vol. 25, SIAM, Philadelphia, PA, USA, 1976.
]Search in Google Scholar
[
[29] Miller K. S., Ross B., An introduction to the fractional calculus and fractional differential equations,Wiley, 1993. 480.
]Search in Google Scholar
[
[30] Podlubny I., Fractional differential equations, vol. 198 of mathematics in science and engineering (1999).
]Search in Google Scholar
[
[31] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, NY, USA, 1962.
]Search in Google Scholar
[
[32] Odibat Z., and Baleanu D., (2020). Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives. Applied Numerical Mathematics, 156, 94-105.10.1016/j.apnum.2020.04.015
]Search in Google Scholar
[
[33] Sardar T., Rana S., Chattopadhyay J. A mathematical model of dengue transmission with memory Commun Nonlinear Sci Numer Simul, 22 (1-3) (2015), pp. 511-52510.1016/j.cnsns.2014.08.009
]Search in Google Scholar
[
[34] Shabir A., ULLAH A., AL-MDALLAL Q.M., et al. Fractional order mathematical modeling of COVID-19 transmission. Chaos, Solitons and Fractals, 2020, vol. 139, p. 110256.10.1016/j.chaos.2020.110256746694732905156
]Search in Google Scholar
[
[35] SHAH K., JARAD F., and Thabet A., On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative. Alexandria Engineering Journal, 2020, vol. 59, no 4, p. 2305-2313.10.1016/j.aej.2020.02.022
]Search in Google Scholar
[
[36] Shaiful E. M., Utoyo M.I., et al. A fractional-order model for HIV dynamics in a two-sex population Int J Math Math Sci, 2018 (2018), Article 6801475, 10.1155/2018/6801475 11 pages.10.1155/2018/6801475
]Search in Google Scholar
[
[37] Shi R., Li Y., and Wang, C. (2020). Stability analysis and optimal. control of a fractional-order model for African swine fever. Virus Research, 288, 19811110.1016/j.virusres.2020.198111
]Search in Google Scholar
[
[38] Sweilam N. H., Al-Mekhlafi S. M., Albalawi A. O., and Baleanu, D. (2020). On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach. Advances in Difference Equations, 2020(1), 1-13.
]Search in Google Scholar
[
[39] Ullah S., Khan M. A., Gomez-Aguilar, J.F.: Mathematical formulation of hepatitis B virus with optimal control analysis. Optim. Control Appl. Methods 40(3), 529/544 (2019)10.1002/oca.2493
]Search in Google Scholar
[
[40] Yoo D., Kim H., Lee J. Y., and Yoo H. S. African swine fever: Etiology, epidemiological status in Korea, and perspective on control. J Vet Sci. 2020 Mar;21(2):e38. https://doi.org/10.4142/jvs.2020.21.e38.10.4142/jvs.2020.21.e38711356932233141
]Search in Google Scholar
[
[41] Yusuf A., Mustapha U. T., Sulaiman T. A., Hincal E., and Bayram M., (2021). Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative. Chaos, Solitons and Fractals, 145, 110794.10.1016/j.chaos.2021.110794
]Search in Google Scholar
[
[42] Zeb A., Zaman G., Jung I. H., Khan M. Optimal campaign strategies in fractional-order smoking dynamics Z Naturforschung A, 69 (5-6) (2014), pp. 225-23110.5560/zna.2014-0020
]Search in Google Scholar