# Prabhakar-like fractional viscoelasticity

## TL;DR

This paper introduces a novel linear viscoelastic model using Prabhakar fractional operators, modifying the classical fractional Maxwell model and exploring its connections to existing models and operators.

## Contribution

It proposes a new viscoelastic model based on Prabhakar derivatives and establishes conditions for its equivalence to classical models, linking it to Caputo-Fabrizio operators.

## Key findings

- The model generalizes classical fractional viscoelastic models.
- Parameter choices recover classical models as special cases.
- Links between Prabhakar integrals and Caputo-Fabrizio operators are established.

## 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.