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

Pelin Yaprakdal  Uzun; Kıvanç Uzun; İlknur Koca

doi:10.11121/ijocta.2023.1366

Authors

Pelin Yaprakdal Uzun Department of Mathematics, Institute of Science, Burdur Mehmet Akif Ersoy University, Burdur, Turkey https://orcid.org/0000-0002-3261-2509
Kıvanç Uzun Career Development Practice and Research Center, Burdur Mehmet Akif Ersoy University, Burdur, Turkey https://orcid.org/0000-0002-6816-1789
İlknur Koca Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Mugla, Turkey https://orcid.org/0000-0003-4393-1588

DOI:

https://doi.org/10.11121/ijocta.2023.1366

Keywords:

Academic achievement, Fractional differential equation, Crossover behaviour, Numerical simulation

Abstract

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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Author Biographies

Pelin Yaprakdal Uzun, Department of Mathematics, Institute of Science, Burdur Mehmet Akif Ersoy University, Burdur, Turkey

Pelin Yaprakdal Uzun received her undergraduate degree in mathematics from Gazi University in 2016 and her master's degree in mathematics from Burdur Mehmet Akif Ersoy University in 2019. She is currently studying for her doctorate at Burdur Mehmet Akif Ersoy University. She has been working as a mathematics teacher in various schools since 2016. Her main field of study is fractional calculus.

Kıvanç Uzun, Career Development Practice and Research Center, Burdur Mehmet Akif Ersoy University, Burdur, Turkey

Kıvanç Uzun received his undergraduate degree in 2014 and his master's degree in 2016 from the Guidance and Psychological Counseling program of Burdur Mehmet Akif Ersoy University. He is currently continuing his doctoral studies at the same university. Between 2014-2020, he worked as a school psychological counselor in various schools affiliated to the Ministry of National Education. He has been working as a lecturer at Burdur Mehmet Akif Ersoy University since 2020. Its main field of study is preventive and intervention services to support the psychological health of adolescents.

İlknur Koca, Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Mugla, Turkey

Ilknur Koca received the B.Sc. and M.Sc. degrees in 2007 and 2009 from the Department of Mathematics from Ankara University, Turkey respectively. She received her Ph.D. degree from the same university in 2013. She is working as an Associate Professor at the Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Mugla, Turkey. Her research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, and iterative methods.

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