Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order
A time-fractional substantial diffusion equation of variable order is investigated, in which the variable-order fractional substantial derivative accommodates the memory effects and the structure change of the surroundings of the physical processes with respect to time. The existence and uniqueness...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-02-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/2/114 |
| _version_ | 1797480096461750272 |
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| author | Xiangcheng Zheng Hong Wang Xu Guo |
| author_facet | Xiangcheng Zheng Hong Wang Xu Guo |
| author_sort | Xiangcheng Zheng |
| collection | DOAJ |
| description | A time-fractional substantial diffusion equation of variable order is investigated, in which the variable-order fractional substantial derivative accommodates the memory effects and the structure change of the surroundings of the physical processes with respect to time. The existence and uniqueness of the solutions to the proposed model are proved, based on which the weighted high-order regularity of the solutions, in which the weight function characterizes the singularity of the solutions, are analyzed. |
| first_indexed | 2024-03-09T21:55:13Z |
| format | Article |
| id | doaj.art-ea1708a82aa9499fb7143110a1107a30 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:13Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-ea1708a82aa9499fb7143110a1107a302023-11-23T19:59:25ZengMDPI AGFractal and Fractional2504-31102022-02-016211410.3390/fractalfract6020114Analysis of a Time-Fractional Substantial Diffusion Equation of Variable OrderXiangcheng Zheng0Hong Wang1Xu Guo2School of Mathematical Sciences, Peking University, Beijing 100871, ChinaDepartment of Mathematics, University of South Carolina, Columbia, SC 29208, USAGeotechnical and Structural Engineering Research Center, Shandong University, Jinan 250100, ChinaA time-fractional substantial diffusion equation of variable order is investigated, in which the variable-order fractional substantial derivative accommodates the memory effects and the structure change of the surroundings of the physical processes with respect to time. The existence and uniqueness of the solutions to the proposed model are proved, based on which the weighted high-order regularity of the solutions, in which the weight function characterizes the singularity of the solutions, are analyzed.https://www.mdpi.com/2504-3110/6/2/114time-fractional diffusion equationfractional substantial derivativevariable-orderexistence and uniquenessregularity |
| spellingShingle | Xiangcheng Zheng Hong Wang Xu Guo Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order Fractal and Fractional time-fractional diffusion equation fractional substantial derivative variable-order existence and uniqueness regularity |
| title | Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order |
| title_full | Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order |
| title_fullStr | Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order |
| title_full_unstemmed | Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order |
| title_short | Analysis of a Time-Fractional Substantial Diffusion Equation of Variable Order |
| title_sort | analysis of a time fractional substantial diffusion equation of variable order |
| topic | time-fractional diffusion equation fractional substantial derivative variable-order existence and uniqueness regularity |
| url | https://www.mdpi.com/2504-3110/6/2/114 |
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