Prabhakar-like fractional viscoelasticity

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.

9 pages

References in corpus (4)

• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• On infinite order differential operators in fractional viscoelasticity
• On the propagation of transient waves in a viscoelastic Bessel medium
• On transient waves in linear viscoelasticity

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• The fractional Dodson diffusion equation: a new approach
• On transient waves in linear viscoelasticity
• Stability of fractional-order systems with Prabhakar derivatives
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• Passive two-plateau relaxation from Tricomi confluent hypergeometric kernels
• Anomalous relaxation in dielectrics with Hilfer fractional derivative