Grey Time Power Model with Caputo Fractional Derivative
In this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-tangent-function transformation is used to improve...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-12-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/1/25 |
| _version_ | 1797343933629464576 |
|---|---|
| author | Pan Hu Chuan-Yun Gu |
| author_facet | Pan Hu Chuan-Yun Gu |
| author_sort | Pan Hu |
| collection | DOAJ |
| description | In this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-tangent-function transformation is used to improve the smoothness of the data sequence, and a grey time power model is obtained, which has higher accuracy than the sinusoidal-function transformation, negative-exponential-function transformation and logarithmic-function transformation. The form and application range of the model are generalized. |
| first_indexed | 2024-03-08T10:54:59Z |
| format | Article |
| id | doaj.art-1b873710ecbe4b959040b6ef24c9e7ef |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:54:59Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-1b873710ecbe4b959040b6ef24c9e7ef2024-01-26T16:35:15ZengMDPI AGFractal and Fractional2504-31102023-12-01812510.3390/fractalfract8010025Grey Time Power Model with Caputo Fractional DerivativePan Hu0Chuan-Yun Gu1School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, ChinaSchool of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, ChinaIn this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-tangent-function transformation is used to improve the smoothness of the data sequence, and a grey time power model is obtained, which has higher accuracy than the sinusoidal-function transformation, negative-exponential-function transformation and logarithmic-function transformation. The form and application range of the model are generalized.https://www.mdpi.com/2504-3110/8/1/25grey time power modelCaputo fractional derivativeLaplace transformlinear-tangent-function transformationsmooth ratio |
| spellingShingle | Pan Hu Chuan-Yun Gu Grey Time Power Model with Caputo Fractional Derivative Fractal and Fractional grey time power model Caputo fractional derivative Laplace transform linear-tangent-function transformation smooth ratio |
| title | Grey Time Power Model with Caputo Fractional Derivative |
| title_full | Grey Time Power Model with Caputo Fractional Derivative |
| title_fullStr | Grey Time Power Model with Caputo Fractional Derivative |
| title_full_unstemmed | Grey Time Power Model with Caputo Fractional Derivative |
| title_short | Grey Time Power Model with Caputo Fractional Derivative |
| title_sort | grey time power model with caputo fractional derivative |
| topic | grey time power model Caputo fractional derivative Laplace transform linear-tangent-function transformation smooth ratio |
| url | https://www.mdpi.com/2504-3110/8/1/25 |
| work_keys_str_mv | AT panhu greytimepowermodelwithcaputofractionalderivative AT chuanyungu greytimepowermodelwithcaputofractionalderivative |