Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution
The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and impli...
| Main Authors: | , , , , |
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| 格式: | 文件 |
| 语言: | English |
| 出版: |
Elsevier
2017
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| 在线阅读: | http://psasir.upm.edu.my/id/eprint/63625/1/Uncertain%20viscoelastic%20models%20with%20fractional%20order.pdf |
| _version_ | 1825932632833130496 |
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| author | Ahmadian, A. Ismail, F. Salahshour, S. Baleanu, D. Ghaemi, F. |
| author_facet | Ahmadian, A. Ismail, F. Salahshour, S. Baleanu, D. Ghaemi, F. |
| author_sort | Ahmadian, A. |
| collection | UPM |
| description | The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed. |
| first_indexed | 2024-03-06T09:45:01Z |
| format | Article |
| id | upm.eprints-63625 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:45:01Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-636252018-11-07T09:03:59Z http://psasir.upm.edu.my/id/eprint/63625/ Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution Ahmadian, A. Ismail, F. Salahshour, S. Baleanu, D. Ghaemi, F. The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed. Elsevier 2017-12 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/63625/1/Uncertain%20viscoelastic%20models%20with%20fractional%20order.pdf Ahmadian, A. and Ismail, F. and Salahshour, S. and Baleanu, D. and Ghaemi, F. (2017) Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution. Communications in Nonlinear Science and Numerical Simulation, 53. 44 - 64. ISSN 1007-5704 10.1016/j.cnsns.2017.03.012 |
| spellingShingle | Ahmadian, A. Ismail, F. Salahshour, S. Baleanu, D. Ghaemi, F. Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title | Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title_full | Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title_fullStr | Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title_full_unstemmed | Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title_short | Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution |
| title_sort | uncertain viscoelastic models with fractional order a new spectral tau method to study the numerical simulations of the solution |
| url | http://psasir.upm.edu.my/id/eprint/63625/1/Uncertain%20viscoelastic%20models%20with%20fractional%20order.pdf |
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