Fractional Modeling for Improving Scholastic Performance of Students with Optimal Control

Abdullahi Yusuf1,2, Sania Qureshi3,4, Umar Tasiu Mustapha5, Salihu S. Musa6,7, Tukur Abdulkadir Sulaıman8,5
1Biruni University
2Federal University Dutse
3Department of Mathematics, Near East University TRNC, Mersin 10, Turkey
4Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
5Department of Mathematics, Science Faculty, Federal University Dutse, Dutse, Nigeria
6Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
7Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
8Department of Computer Engineering, Biruni University, İstanbul, Turkey

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Tài liệu tham khảo

Zarb, J.M.: A comparison of remedial, failure and successful secondary school students across self-perception and past and present school performance variables. Adolescence 19(74), 335–348 (1984)

Aysan, F., Tanriogen, G., Abdurrahman, G.: Perceived causes of academic failure among the students at the faculty of education at Buca. Educ. Resour. Inf. Center 406(326), 20 (1996)

HEFCE.: Undergraduate non-completion in Higher education in England. Technical report 97(29) (1997)

Adeyemi, A.M., Semiu, A.B.: Institutional factors as predictors of students academic achievement in colleges of education in South Western Nigeria. Int. J. Educ. Admin. Pol. Stud. 6(8), 141–153 (2014)

Jackson, K.M., Sher, K.J., Park, A.: Drinking among college students: consumption and consequences. In: Galanter, M. (ed.) Alcohol Problems in Adolescents and Young Adults: Epidemiology, Neurobiology, Prevention, and Treatment, pp. 85–117. Springer, Berlin (2006)

Straus, R., Bacon, S.D.: Drinking in College. Yale University Press, New Haven (1953)

Murphy, J.G., MacKillop, J.: Relative reinforcing efficacy of alcohol among college student drinkers. Exp. Clin. Psychopharmacol. 14(2), 219 (2006)

Wechsler, H., Davenport, A., Dowdall, G., Moeykens, B., Castillo, S.: Health and behavioral consequences of binge drinking in college. J. Am. Med. Assoc. 272, 1672–1677 (1994)

Kermack, W.O., Mckendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A. 115, 700–721 (1927)

Benedict, B.: Modelling alcohol as a contagious disease: how infected drinking buddies spread problem drinking. SIAM News. 40, 8 (2007)

Bettencourt, L.M.A., Cintron-Arias, A., Kaiser, D.I., Castillo-Chavez, C.: The power of good idea: quantitative modeling of ideas from epidemiological models. Phys. A 364, 513–536 (2006)

Gonzalez, B., Huerta-Sanchez, E., Ortiz-Nieves, A., Vazquez-Alvarez, T., Kribs-Zaleta, C.: Am I too fat? Bulimia as an epidemic. J. Math. Psychol. 47, 515–526 (2003)

Mantheya, J.L., Aidoo, A.Y., Ward, K.Y.: Campus drinking: an epidemiological model. J. Biol. Dyn. 2(3), 346–356 (2008)

Usaini, S., Mustapha, U.T., Sabiu, S.M.: Modelling scholastic underachievement as a contagious disease. Math. Methods Appl. Sci. (2018). https://doi.org/10.1002/mma.4924

Carvalho, A.R., Pinto, C.M., Baleanu, D.: HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load. Adv. Differ. Equ. 2018(1), 2 (2018)

Kumar, D., Singh, J., Al Qurashi, M., Baleanu, D.: A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying. Adv. Differ. Equ. 2019(1), 278 (2019)

Baleanu, D., Raza, A., Rafiq, M., Arif, M.S., Ali, M.A.: Competitive analysis for stochastic influenza model with constant vaccination strategy. IET Syst. Biol. 13(6), 316–326 (2019)

Baleanu, D., Jajarmi, A., Bonyah, E., Hajipour, M.: New aspects of poor nutrition in the life cycle within the fractional calculus. Adv. Differ. Equ. 2018(1), 230 (2018)

Alqahtani, R.T., Yusuf, A., Agarwal, R.P.: Mathematical analysis of oxygen uptake rate in continuous process under Caputo derivative. Mathematics 9, 675 (2021). https://doi.org/10.3390/math9060675

Memon, Z., Qureshi, S., Memon, B.R.: Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: a case study. Chaos Solitons Fractals 144, 110655 (2021)

Yusuf, A., Mustapha, U.T., Sulaiman, T.A., Hincal, E., Bayrama, M.: Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative. Chaos Solitons Fractals 145, 110794 (2021)

Ahmed, I., Goufo, E.F.D., Yusuf, A., Kumam, P., Chaipanya, P., Nonlaopon, K.: An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC fractional operator. Alex. Eng. J. 60, 2979–2995 (2021)

Mustapha, U.T., Qureshi, S., Yusuf, A., Hincal, E.: Fractional modeling for the spread of Hookworm infection under Caputo operator. Chaos Solitons Fractals 137, 109878 (2020)

Qureshi, S., Jan, R.: Modeling of measles epidemic with optimized fractional order under Caputo differential operator. Chaos Solitons Fractals 145, 110766 (2021)

Qureshi, S., Atangana, A.: Mathematical analysis of dengue fever outbreak by novel fractional operators with field data. Physica A 526, 121127 (2019)

Sania, Q., Yusuf, A.: Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator. Chaos Solitons Fractals 126, 32–40 (2019)

Qureshi, S., Yusuf, A., Aziz, S.: Fractional numerical dynamics for the logistic population growth model under Conformable Caputo: a case study with real observations. Phys. Scr. 96, 114002 (2021). https://doi.org/10.1088/1402-4896/ac13e0

Abdon, A.: Convergence and stability analysis of a novel iteration method for fractional biological population equation. Neural Comput. Appl. 25(5), 1021–1030 (2014)

Abdon, A., Alabaraoye, E.: Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller–Segel equations. Adv. Differ. Equ. 2013(1), 94 (2013)

Badr, S.T.A., Atangana, A., Koca, I.: A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel. Adv. Mech. Eng. 8(11), 1687814016681906 (2016)

Yusuf, A., et al.: Two-strain epidemic model involving fractional derivative with Mittag–Leffler kernel. Chaos Interdiscip. J. Nonlinear Sci. 28(12), 123121 (2018)

Alkahtani, B.S.T., Atangana, A.: Modeling the potential energy field caused by mass density distribution with Eton approach. Open Phys. 14(1), 106–113 (2016)

Atangana, A.: A novel model for the lassa hemorrhagic fever: deathly disease for pregnant women. Neural Comput. Appl. 26(8), 1895–1903 (2015)

Losada, J., Nieto, J.: Fractional integral associted to fractional derivatives with nonsingular kernels. Progr. Fract. Differ. Appl 7(3), 1–7 (2021)

Baskonus, H.M., Bulut, H. (2016). Regarding on the prototype solutions for the nonlinear fractional-order biological population model. In: AIP Conference Proceedings, vol. 1738, No. 1, pp. 290004. AIP Publishing LLC

Caputo, M., Fabrizio, M.: On the singular kernels for fractional derivatives some applications to partial differential equations. Progr. Fract. Differ. Appl. 7(2), 1–4 (2021)

Shiri, B., Wu, G.C., Baleanu, D.: Collocation methods for terminal value problems of tempered fractional differential equations. Appl. Numer. Math. 156, 385–395 (2020)

Ameen, I., Baleanu, D., Ali, H.M.: An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment. Chaos Solitons Fractals 137, 109892 (2020)

Baskonus, H.M., Bulut, H.: On the numerical solutions of some fractional ordinary differential equations by fractional Adams–Bashforth–Moulton method. Open Math. 13(1) (2015)

Baleanu, D., Sajjadi, S.S., Jajarmi, A., Defterli, Ö.: On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control. Adv. Differ. Equ. 2021(1), 234 (2021)

Baleanu, D., Sajjadi, S.S., Asad, J.H., Jajarmi, A., Estiri, E.: Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system. Adv. Differ. Equ. 2021(1), 157 (2021)

Baleanu, D., Sajjadi, S.S., Jajarmi, A., Defterli, O., Asad, J.H.: The fractional dynamics of a linear triatomic molecule. Rom. Rep. Phys. 73(1), 105 (2021)

Baleanu, D., Ghanbari, B., Asad, J.H., Jajarmi, A., Pirouz, H.M.: Planar system-masses in an equilateral triangle: numerical study within fractional calculus. CMES Comput. Model. Eng. Sci. 124(3), 953–968 (2020)

Jajarmi, A., Baleanu, D.: On the fractional optimal control problems with a general derivative operator. Asian J. Control 23(2), 1062–1071 (2021)

Li, C., Zeng, F.: Numerical Methods for Fractional Calculus. Chapman and Hall/CRC, London (2015)

Jajarmi, A., Baleanu, D.: A new fractional analysis on the interaction of HIV with CD4+ T-cells. Chaos Solitons Fractals 113, 221–229 (2018)

Baleanu, D., Jajarmi, A., Hajipour, M.: On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dyn. 94(1), 397–414 (2018)

Farouk, T.S., Evren, H.: An optimal control approach for the interaction of immune checkpoints, immune system, and BCG in the treatment of superficial bladder cancer. Eur. Phys. J. Plus 133, 241 (2018)

Qureshi, S., Ramos, H.: L-stable explicit nonlinear method with constant and variable step-size formulation for solving initial value problems. Int. J. Nonlinear Sci. Numer. Simul. 19(7–8), 741–751 (2018)

Emmanuel, F.S., Qureshi, S.: Convergent numerical method using transcendental function of exponential type to solve continuous dynamical systems. J. Math. 51(10), 45–56 (2019)

Qureshi, S., Emmanuel, F.S.: Convergence of a numerical technique via interpolating function to approximate physical dynamical systems. J. Adv. Phys. 7(3), 446–450 (2018)

Aliya, T., Shaikh, A.A., Qureshi, S.: Development of a nonlinear hybrid numerical method. Adv. Differ. Equ. Control Process. 19(3), 275–285 (2018)

Veeresha, P., Ilhan, E., Baskonus, H.M.: Fractional approach for analysis of the model describing wind-influenced projectile motion. Phys. Scr. 96(7), 075209 (2021). https://doi.org/10.1088/1402-4896/abf868