A note on a modified fractional Maxwell model

R. Garra, A. Consiglio and F. Mainardi

Chaos, Solitons & Fractals, 2022, vol. 163, issue C

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.

Keywords: Linear viscoelasticity; Creep; Relaxation; Hadamard fractional derivative; Fractional calculus; Ultra slow kinetics (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007391

DOI: 10.1016/j.chaos.2022.112544

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