Prabhakar-like Fractional Viscoelasticity
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Abstract
The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the Prabhakar one. Furthermore, we also discuss how to recover a formal equivalence between the new model and the known classical models of linear viscoelasticity by means of a suitable choice of the parameters in the Prabhakar derivative. Moreover, we also underline an interesting connection between the theory of Prabhakar fractional integrals and the recently introduced Caputo-Fabrizio differential operator.Keywords
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This publication has 13 references indexed in Scilit:
- On transient waves in linear viscoelasticityWave Motion, 2017
- On the propagation of transient waves in a viscoelastic Bessel mediumZeitschrift für angewandte Mathematik und Physik, 2017
- On infinite series concerning zeros of Bessel functions of the first kindThe European Physical Journal Plus, 2016
- A class of linear viscoelastic models based on Bessel functionsMeccanica, 2016
- A dynamic viscoelastic analogy for fluid-filled elastic tubesMeccanica, 2016
- Fractional Maxwell fluid with fractional derivative without singular kernelThermal Science, 2016
- On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectricsJournal of Computational Physics, 2015
- Hilfer–Prabhakar derivatives and some applicationsApplied Mathematics and Computation, 2014
- Creep, relaxation and viscosity properties for basic fractional models in rheologyThe European Physical Journal Special Topics, 2011
- Mittag‐Leffler Functions and Their ApplicationsJournal of Applied Mathematics, 2011