# On infinite order differential operators in fractional viscoelasticity

## TL;DR

This paper explores the properties of viscoelastic models characterized by infinite derivatives, focusing on Bessel models that mimic fractional Maxwell behavior at short times, advancing understanding of complex material responses.

## Contribution

It introduces and analyzes properties of viscoelastic models with infinite derivatives, specifically examining Bessel models and their fractional Maxwell-like behavior.

## Key findings

- Bessel models exhibit fractional Maxwell behavior at short times
- Models involve both integer and fractional order derivatives
- Provides insights into complex viscoelastic responses

## Abstract

In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the recently developed Bessel models of linear viscoelasticiy that, for short times, behave like fractional Maxwell bodies of order $1/2$.