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

<p>This paper uses the principle of compressed mapping to discuss the existence and uniqueness of the explicit finite difference method for the fractional diffusion equation with time delay. The Laplace transform method obtains the necessary expression form of the solution. At the same time, the existence theorem and the existence and uniqueness theorem of the solution to the boundary value problem is established. Finally, an example is given to verify the correctness of the conclusion. The experimental results show that the parallel algorithm proposed in this paper agrees with the exact solution.</p>
</abstract>

This paper uses the principle of compressed mapping to discuss the existence and uniqueness of the explicit finite difference method for the fractional diffusion equation with time delay. The Laplace transform method obtains the necessary expression form of the solution. At the same time, the existence theorem and the existence and uniqueness theorem of the solution to the boundary value problem is established. Finally, an example is given to verify the correctness of the conclusion. The experimental results show that the parallel algorithm proposed in this paper agrees with the exact solution.

The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping

Applied Mathematics and Nonlinear Sciences

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

This paper uses the principle of compressed mapping to discuss the existence and uniqueness of the explicit finite difference method for the fractional...

The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping

Published Online: Jun 06, 2023

Page range: 331 - 338

Received: Jan 07, 2022

Accepted: Mar 29, 2022

DOI: https://doi.org/10.2478/amns.2022.2.00014

Keywords
Fractional differential equations, Principle of contraction mapping, College mathematics, Fractional Riesz

© 2023 Dong Zhang et al., published by Sciendo

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

Figure 1

Figure 2

The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping

Published Online: Jun 06, 2023

Page range: 331 - 338

Received: Jan 07, 2022

Accepted: Mar 29, 2022

DOI: https://doi.org/10.2478/amns.2022.2.00014

KeywordsFractional differential equations, Principle of contraction mapping, College mathematics, Fractional Riesz

© 2023 Dong Zhang et al., published by Sciendo

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

Figure 1

Figure 2

Keywords
Fractional differential equations, Principle of contraction mapping, College mathematics, Fractional Riesz