The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors

The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors

Academic achievement is very important, as it enables students to be well-equipped for professional and social life and shapes their future. In the case of a possible academic failure, students generally face many cognitive, social, psychological, and behavioral problems. This problem experienced by the students has been addressed with the mathematical model in this study. This mathematical model will be handled with the help of the fractional operator, and the existence, uniqueness, and positivity of the solutions to the model equation system will be examined. In addition, local and global stability analyses of the equilibrium points of the model are planned. Numerical simulations are performed with different values of fractional orders and densities of randomness. This study is very important in terms of its original and multidisciplinary approach to a subject in the field of social sciences.

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  • Nartgun, S., & Cakir, M. (2014). Examining the high school students’ academic achievement in terms of academic motivation and academic procrastination. Journal of Research in Education and Teaching, 3 (3), 379-391.
  • Carter, V., & Good, E. (1973). Dictionary of education (4th ed.). New York: McGraw Hill Book Company.
  • Kenc, M. F., & Oktay, B. (2002). The relationship between academic self-concept and academic success.Education and Science, 27(124), 71-79.
  • Ozguven, I. E. (2014). Psychological tests [Psikolojik testler] (12th ed.). Ankara: Nobel Akademik Yayincilik.
  • York, T. T., Gibson, C., & Rankin, S. (2015). Defining and measuring academic success. Practical Assessment, Research, and Evaluation, 20(1), 1-20.
  • Kasatura, I. (1991). From school success to life success [Okul basarisindan hayat basarisina]. Istanbul: Altin Kitaplar Yayinevi.
  • Sarier, Y. (2016). The factors that affects students’ academic achievement in Turkey: A meta-analysis study. Hacettepe University Journal of Education, 31(3), 609-627.
  • Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman and Company.
  • Bong, M. (1995). Epistemological beliefs and generalizability of self-efficacy: Implications for instructional design (Unpublished doctoral dissertation). University of Southern California, California.
  • Uzun, K., & Karatas, Z. (2020). Predictors of academic self efficacy: Intolerance of uncertainty, positive beliefs about worry and academic locus of control. International Education Studies, 13(6), 104-116.
  • Komarraju, M., & Nadler, D. (2013). Self-efficacy and academic achievement: Why do implicit beliefs, goals, and effort regulation matter?, Learning and Individual Differences, 25, 67-72.
  • Alivernini, F., & Lucidi, F. (2011). Relationship between social context, self-efficacy, motivation, academic achievement, and intention to drop out of high school: A longitudinal study. The Journal of Educational Research, 104(4), 241-252.
  • Bandura, A. (1982). Self-efficacy mechanism in human agency. American Psychologist, 37 (2), 122-147.
  • Akandere, M., Ozyalvac, N. T., & Duman, S. (2010). The attitudes of the students in secondary education to physical education lesson and the investigation of their success motivations: Konya anatolian high school sample. The Journal of Selcuk University Social Sciences Institute, (24), 1- 10.
  • Rosenberg, M. (1965). Society and the adolescent self-image. New Jersey: Princeton University Press.
  • Sharma, P., & Sharma, M. (2021). Relationship between self-esteem and academic achievement of secondary school students. Elementary Education Online, 20(1), 3208-3212.
  • Deveci, T. (2021). The effects of family structure on the individual’s motivation for academic success, academic permission and the level of happiness: Erzincan center and Tercan district example (Unpublished master’s thesis). Sivas Cumhuriyet University, Graduate School of Social Sciences, Sivas.
  • Senturk, M. (2019).Analysis of the effect of family factor on academic achievement of primary school students (Unpublished master’s thesis). Canakkale Onsekiz Mart University, Graduate School of Educational Sciences, Canakkale.
  • Glasser, W. (2012). Schools without fail. New York: HarperCollins Publishers.
  • Tezel-Sahin, F., & Ozyurek, A. (2008). Examining of the effects to child raising attitudes of demographic characteristics of parents that have 5-6 years children group. The Journal of Turkish Educational Sciences, 6(3), 395-414.
  • Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75(3), 417-453.
  • Akyol, G., Sungur, S., & Tekkaya, C. (2010). The contribution of cognitive and metacognitive strategy use to students’ science achievement. Educational Research and Evaluation, 16(1), 1-21.
  • Koutsoulis, M. K., & Campbell, J. R. (2001). Family processes affect students’ motivation, and science and math achievement in Cypriot high schools. Structural Equation Modeling: A Multi-disciplinary Journal, 8(1), 108-127.
  • Preble, B., & Gordon, R. (2011). Transforming school climate and learning-beyond bullying and compliance. California, USA: Corwin A Sage Company.
  • Demirtas, Z. (2010). The relationship between school culture and student achievement. Education and Science, 35 (158), 3-13.
  • Kizildag, S. (2009). Loneliness, submissive acts and social support as the determiners of academic success (Unpublished master’s thesis). Hacettepe University, Graduate School of Social Sciences, Ankara.
  • Sisman, M. (2018). Teaching leadership [Ogretim liderligi] (6th ed.). Ankara: Pegem Akademi Yayincilik.
  • Wikipedia (2022). Mathematical model. Access address (01.08.2022): https://en.wikipedia.org/wiki/Mathematical_model
  • Sheergojri, A. R., Iqbal, P., Agarwal, P., & Ozdemir, N. (2022). Uncertainty-based Gompertz growth model for tumor population and its numerical analysis. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12(2), 137-150.
  • Benson, D. A., Wheatcraft, S. W., & Meerschaert, M. M. (2000). Application of a fractional advection-dispersion equation. Water Resources Research, 36(6), 1403-1412.
  • Koca, I. (2019). Modeling the heat flow equation with fractional-fractal differentiation. Chaos, Solitons & Fractals, 128, 83-91.
  • Evirgen F. (2023). Transmission of Nipah virus dynamics under Caputo fractional derivative, Journal of Computational and Applied. Mathematics, 418, Article 114654.
  • Ucar E., Ozdemir N., Altun E. (2023) Qualitative analysis and numerical simulations of new model describing cancer, Journal of Computational and Applied. Mathematics, 422, Article 114899.
  • Yusuf, A., Qureshi, S., Mustapha, U. T., Musa, S. S., & Sulaiman, T. A. (2022). Fractional modeling for improving scholastic performance of students with optimal control. International Journal of Applied and Computational Mathematics, 8(1), 1-20.
  • Ross, B. (1975). A brief history and exposition of the fundamental theory of fractional calculus. Fractional Calculus and its Applications, 57, 1-36.
  • Atangana, A., & Igret-Araz, S. (2021). New concept in calculus: Piecewise differential and integral operators. Chaos, Solitons & Fractals, 145, 110638.
  • Podlubny, I. (1998). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press: Cambridge, MA, USA.
  • Atangana, A. (2021). Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world? Advances in Difference Equations, 2021, 403.
  • Debnath, L. (2004). A brief historical introduction to fractional calculus. International Journal of Mathematical Education in Science and Technology, 35(4), 487-501.
  • Toufik, M., Atangana, A. (2017). New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models.The European Physical Journal Plus, 132(10), 444.
  • Dinc, A. R. (2017). Relationship between the students who educated at a boarding highschool both daytime and boarding education and perceived parents support level (Unpublished master’s thesis). Hasan Kalyoncu University, Graduate School of Social Sciences, Gaziantep.
An International Journal of Optimization and Control: Theories & Applications (IJOCTA)-Cover
  • ISSN: 2146-0957
  • Yayın Aralığı: Yılda 2 Sayı
  • Yayıncı: Prof. Dr. Ramazan YAMAN
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The solvability of the optimal control problem for a nonlinear Schrödinger equation

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