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

Uzun P. Y., Uzun K., Koca I.

International Journal of Optimization and Control: Theories and Applications, cilt.13, sa.2, ss.244-258, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.11121/ijocta.2023.1366
  • Dergi Adı: International Journal of Optimization and Control: Theories and Applications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Communication Abstracts, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.244-258
  • Anahtar Kelimeler: Academic achievement, Crossover behaviour, Fractional differential equation, Numerical simulation
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.