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A variable-order fractional differential equation model of shape memory polymers

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  • Li, Zheng
  • Wang, Hong
  • Xiao, Rui
  • Yang, Su

Abstract

A shape-memory polymer (SMP) is capable of memorizing its original shape, and can acquire a temporary shape upon deformation and returns to its permanent shape in response to an external stimulus such as a temperature change. SMPs have been widely used industrial and medical applications. Previously, differential equation models were developed to describe SMPs and their applications. However, these models are often of very complicated form, which require accurate numerical simulations.

Suggested Citation

  • Li, Zheng & Wang, Hong & Xiao, Rui & Yang, Su, 2017. "A variable-order fractional differential equation model of shape memory polymers," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 473-485.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:473-485
    DOI: 10.1016/j.chaos.2017.04.042
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Jianping Liu & Xia Li & Limeng Wu, 2016. "An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-9, June.
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    Cited by:

    1. Cao, Jiawei & Chen, Yiming & Wang, Yuanhui & Cheng, Gang & Barrière, Thierry, 2020. "Shifted Legendre polynomials algorithm used for the dynamic analysis of PMMA viscoelastic beam with an improved fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Zhang, Zhi-Yong & Liu, Cheng-Bao, 2022. "Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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