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A note on a modified fractional Maxwell model

Author

Listed:
  • Garra, R.
  • Consiglio, A.
  • Mainardi, F.

Abstract

In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that we can take into account at the same time memory effects and the time-dependence of the viscosity coefficient. We obtain an ultra-slow relaxation response whose explicit analytic form is given by the Mittag-Leffler function with a logarithmic argument. We show graphically the main properties of this relaxation response, also with the asymptotic behaviour.

Suggested Citation

  • Garra, R. & Consiglio, A. & Mainardi, F., 2022. "A note on a modified fractional Maxwell model," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007391
    DOI: 10.1016/j.chaos.2022.112544
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    References listed on IDEAS

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    1. Garra, Roberto & Mainardi, Francesco & Spada, Giorgio, 2017. "A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 333-338.
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    Cited by:

    1. Li, Jing & Ma, Li, 2023. "A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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