The thesis applies solutions to boundary value problems of a class of fractional differential equation coupled systems with a p-Laplacian operator. This article applies this part of the content to alleviate the psychological barriers of college students. This article transforms the tendency of individual consciousness in college students’ psychological counselling into a problem of solving boundary value problems of fractional differential equations. Studies have shown that using fractional differential equations to analyse the causes of college students’ psychological barriers has an essential role in eliminating college students’ psychological barriers.

This article proposes a nonlinear mental health evaluation model after combining the nonlinear finite element equation with the mental health education of teachers in colleges and universities. We take the “self-concept” in psychology as an order parameter to judge mental health. At the same time, logical thinking is used to guide college teachers to rethink the process of their psychological activities. Research has found that the nature of human psychology is nonlinear. It is feasible to use nonlinear analysis methods to improve the status quo of original data analysis in psychological and behavioral control research.