МОДЕЛЮВАННЯ ПРОЦЕСУ НАУЧІННЯ НА ОСНОВІ ВИКОРИСТАННЯ ДИФЕРЕНЦІАЛЬНИХ РІВНЯНЬ ДРОБОВИХ ПОРЯДКІВ

Abstract

This article is an integrated study conducted to develop a learning model which would make it possible to identify the students' changes of knowledge, abilities and skills acquisition over time as well as the formation of special features of their individual background. The authors have demonstrated how the traditional system of students' learning and cognitive activity management can be improved. Also, they have justified the application of the cybernetic model based on fractional equations for the description and evaluation of the student's learning process. As a result of the findings, students who assimilate the content of teaching information and form personal experience in different ways have compiled different groups; the learning curve constructed on the basis of the heterogeneous differential equation of second order with integer powers has been compared with the set of models with equations of fractional order of aperiodic and fractional power components.