The learning process simulation based on differential equations of fractional orders - Oleksii P. Chornyi; Larysa V. Herasymenko; Victor V. Busher (Academy of Cognitive and Natural Sciences, 2021)
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. Authors have justified the application of the cybernetic model based on fractional equations for the description and evaluation of the student's learning process. Learning is dealt as a transformation of young people's knowledge, abilities and skills into a complex background, which envisages its implementation in the future professional activity. The advantage of the suggested model is better approximation characteristics which allow the consideration of a wide range of factors affecting the learning process including the youth's neurodynamic and psychological nature. The research has employed both mathematical modeling methods and psychodiagnostic techniques (surveys, questionnaires). 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. The prospect of the issue to explore is the improvement of the suggested model considering special characteristics of cognitive processes aimed at the formation of an individual path of the student's learning.