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

<p>This article combines ordinary differential equations’ theoretical and practical characteristics to explore how to integrate mathematical modeling ideas in teaching materials and teaching methods. We apply the fractional differential equation algorithm to the mathematical modeling of Terman diffusion. At the same time, the article proposes a framework for obtaining accurate solutions of a class of nonlinear Sinai stochastic models with power-law diffusion through Mittag-Leffler function transformation. In this way, we have obtained great explicit and accurate solutions of some important Mittag-Leffler function power-law diffusion physical processes.</p>
</abstract>

This article combines ordinary differential equations’ theoretical and practical characteristics to explore how to integrate mathematical modeling ideas in teaching materials and teaching methods. We apply the fractional differential equation algorithm to the mathematical modeling of Terman diffusion. At the same time, the article proposes a framework for obtaining accurate solutions of a class of nonlinear Sinai stochastic models with power-law diffusion through Mittag-Leffler function transformation. In this way, we have obtained great explicit and accurate solutions of some important Mittag-Leffler function power-law diffusion physical processes.

Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching

Hebei University of Economics and Business

Applied Mathematics and Nonlinear Sciences

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

This article combines ordinary differential equations’ theoretical and practical characteristics to explore how to integrate mathematical modeling ideas in...

Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching

Published Online: Jun 11, 2023

Page range: 299 - 308

Received: Jan 22, 2022

Accepted: Mar 18, 2022

DOI: https://doi.org/10.2478/amns.2022.2.00012

Keywords
Fractional differential equations, Very slow diffusion, Mathematical modeling ideas, Sinai stochastic model, Fractional structural derivatives, Teaching

© 2023 Yingwei Chen et al., published by Sciendo

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

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Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching

Published Online: Jun 11, 2023

Page range: 299 - 308

Received: Jan 22, 2022

Accepted: Mar 18, 2022

DOI: https://doi.org/10.2478/amns.2022.2.00012

KeywordsFractional differential equations, Very slow diffusion, Mathematical modeling ideas, Sinai stochastic model, Fractional structural derivatives, Teaching

© 2023 Yingwei Chen et al., published by Sciendo

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

Figure 1

Figure 2

Figure 3

Keywords
Fractional differential equations, Very slow diffusion, Mathematical modeling ideas, Sinai stochastic model, Fractional structural derivatives, Teaching