A Nonlocal Fractional Peridynamic Diffusion Model
This paper proposes a nonlocal fractional peridynamic (FPD) model to characterize the nonlocality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the peridynamic (PD) model. The main idea is to use the fractional Euler–Lagrange formula to establish...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/3/76 |
| _version_ | 1797519239909736448 |
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| author | Yuanyuan Wang HongGuang Sun Siyuan Fan Yan Gu Xiangnan Yu |
| author_facet | Yuanyuan Wang HongGuang Sun Siyuan Fan Yan Gu Xiangnan Yu |
| author_sort | Yuanyuan Wang |
| collection | DOAJ |
| description | This paper proposes a nonlocal fractional peridynamic (FPD) model to characterize the nonlocality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the peridynamic (PD) model. The main idea is to use the fractional Euler–Lagrange formula to establish a peridynamic anomalous diffusion model, in which the classical exponential kernel function is replaced by using a power-law kernel function. Fractional Taylor series expansion was used to construct a fractional peridynamic differential operator method to complete the above model. To explore the properties of the FPD model, the FDM, the PD model and the FPD model are dissected via numerical analysis on a diffusion process in complex media. The FPD model provides a generalized model connecting a local model and a nonlocal model for physical systems. The fractional peridynamic differential operator (FPDDO) method provides a simple and efficient numerical method for solving fractional derivative equations. |
| first_indexed | 2024-03-10T07:40:06Z |
| format | Article |
| id | doaj.art-e0f002f811634e5f98adc4bdf04e1add |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:40:06Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e0f002f811634e5f98adc4bdf04e1add2023-11-22T13:09:11ZengMDPI AGFractal and Fractional2504-31102021-07-01537610.3390/fractalfract5030076A Nonlocal Fractional Peridynamic Diffusion ModelYuanyuan Wang0HongGuang Sun1Siyuan Fan2Yan Gu3Xiangnan Yu4State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, ChinaState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, ChinaCollege of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaState Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, ChinaThis paper proposes a nonlocal fractional peridynamic (FPD) model to characterize the nonlocality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the peridynamic (PD) model. The main idea is to use the fractional Euler–Lagrange formula to establish a peridynamic anomalous diffusion model, in which the classical exponential kernel function is replaced by using a power-law kernel function. Fractional Taylor series expansion was used to construct a fractional peridynamic differential operator method to complete the above model. To explore the properties of the FPD model, the FDM, the PD model and the FPD model are dissected via numerical analysis on a diffusion process in complex media. The FPD model provides a generalized model connecting a local model and a nonlocal model for physical systems. The fractional peridynamic differential operator (FPDDO) method provides a simple and efficient numerical method for solving fractional derivative equations.https://www.mdpi.com/2504-3110/5/3/76fractional peridynamic modeldiffusion processEuler–Lagrange formulaTaylor series expansionnonlocality |
| spellingShingle | Yuanyuan Wang HongGuang Sun Siyuan Fan Yan Gu Xiangnan Yu A Nonlocal Fractional Peridynamic Diffusion Model Fractal and Fractional fractional peridynamic model diffusion process Euler–Lagrange formula Taylor series expansion nonlocality |
| title | A Nonlocal Fractional Peridynamic Diffusion Model |
| title_full | A Nonlocal Fractional Peridynamic Diffusion Model |
| title_fullStr | A Nonlocal Fractional Peridynamic Diffusion Model |
| title_full_unstemmed | A Nonlocal Fractional Peridynamic Diffusion Model |
| title_short | A Nonlocal Fractional Peridynamic Diffusion Model |
| title_sort | nonlocal fractional peridynamic diffusion model |
| topic | fractional peridynamic model diffusion process Euler–Lagrange formula Taylor series expansion nonlocality |
| url | https://www.mdpi.com/2504-3110/5/3/76 |
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