# A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus

Source: [A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus](<https://www.sota2.com/research/paper/68fa35821e209131ce8a20d8>)

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Data updated: 2025-10-24T21:17:23.261Z

Authors: Roberto Garra, Francesco Mainardi, Giorgio Spada

Published: 2017-01-11T17:25:39.000Z

## Abstract

We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter $\\nu \\in (0,1\]$, the logarithmic creep law known in rheology as Lomnitz law (obtained for $\\nu=1$). We derive the constitutive stress-strain relation of this generalized model in a form that couples memory effects and time-varying viscosity. Then, based on the hereditary theory of linear viscoelasticity, we also derive the corresponding relaxation function by solving numerically a Volterra integral equation of the second kind. So doing we provide a full characterization of the new model both in creep and in relaxation representation, where the slow varying functions of logarithmic type play a fundamental role as required in processes of ultra slow kinetics.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1701.03068>)

[PDF](<https://arxiv.org/pdf/1701.03068.pdf>)