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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...

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Main Authors: Ahmadian, A., Ismail, F., Salahshour, S., Baleanu, D., Ghaemi, F.
Format: Article
Language:English
Published: Elsevier 2017
Online Access:http://psasir.upm.edu.my/id/eprint/63625/1/Uncertain%20viscoelastic%20models%20with%20fractional%20order.pdf
http://psasir.upm.edu.my/id/eprint/63625/
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spelling my.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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.
format Article
author Ahmadian, A.
Ismail, F.
Salahshour, S.
Baleanu, D.
Ghaemi, F.
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
author_facet Ahmadian, A.
Ismail, F.
Salahshour, S.
Baleanu, D.
Ghaemi, F.
author_sort Ahmadian, A.
title 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_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_sort uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution
publisher Elsevier
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/63625/1/Uncertain%20viscoelastic%20models%20with%20fractional%20order.pdf
http://psasir.upm.edu.my/id/eprint/63625/
_version_ 1643837847090757632
score 13.211869

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