<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Nonlinear fractional differential equations are an important part of advanced mathematics teaching. The existence and uniqueness of its positive solution have...

The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations

Published Online: Jul 15, 2022

Page range: 861 - 868

Received: Feb 14, 2022

Accepted: Apr 17, 2022

DOI: https://doi.org/10.2478/amns.2022.2.0073

Keywords
Nonlinear differential equations, Applied mathematics, Lyapunov function method, Mathematical modeling, Mathematical teaching model

© 2023 Jie Wu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations

Published Online: Jul 15, 2022

Page range: 861 - 868

Received: Feb 14, 2022

Accepted: Apr 17, 2022

DOI: https://doi.org/10.2478/amns.2022.2.0073

KeywordsNonlinear differential equations, Applied mathematics, Lyapunov function method, Mathematical modeling, Mathematical teaching model

© 2023 Jie Wu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Keywords
Nonlinear differential equations, Applied mathematics, Lyapunov function method, Mathematical modeling, Mathematical teaching model