https://hdl.handle.net/20.500.12809/91 2026-04-05T19:28:08Z https://hdl.handle.net/20.500.12809/10929 The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors Uzun, Pelin Yaprakdal; Uzun, Kıvanç; Koca, İlknur 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. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10918 Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators Koca, İlknur; Atangana, Abdon A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10817 Financial model with chaotic analysis Koca, İlknur Recently, it was proposed to use a brand-new set of nonlinear ordinary differential equations. The system aims to represent chaotic financial activities. Such a system was taken into consideration for various analyses in this paper. For each of the three axes, we first evaluated the nullcline points and then gave the formula for the associated Poincare mapping. With various differential operators, we have analyzed the existence and uniqueness of systems of solutions. We have numerically solved the model using the well-known Nystrom in the case of the classical model and the Midpoint in the case of fractional derivatives. 2023-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/10208 Analysis of a COVID-19 model with nonlocal and stochastic behaviors Koca, İlknur; Atangana, Abdon Systems of nonlinear ordinary differential equations have been employed to model complex behaviors arising in many real-world problems including epidemiology, biology, and many others. Many chaotic behaviors have been modeled using these equations as well as epidemiological problems. To construct these, model differential and integral operators with local and nonlocal features have been used. However, in many instances, it was noted that models with these concepts are unable to replicate accurately complex behaviors with different patterns, thus very recently piecewise operators were suggested and applied in some problems. In this paper, we chose a system of six nonlinear different equations and applied the concept of piecewise derivative. 2022-01-01T00:00:00Z