Nonlinear fractional differential equations are an important part of advanced mathematics teaching. The existence and uniqueness of its positive solution have always been a hot topic of academic discussion. This article uses differential inclusion theory and the Lyapunov stability method to analyze the finite-time stabilization control problem of the discontinuous mathematical adjustment model. The article uses a modified decomposition method and convergence acceleration technology in the application of fractional differential equations. The method gives an analytical approximate solution sequence that is easy to calculate, verify, and quickly converge. Finally, examples of Lyapunov stability and the construction of the V function can inspire students to understand ordinary differential equations and increase their interest in learning.