On Evolutionary Equations with Material Laws Containing Fractional Integrals

TL;DR

This paper establishes well-posedness for a class of evolutionary equations involving fractional integrals in material laws, with an application to a Kelvin-Voigt model, advancing understanding of fractional calculus in material modeling.

Contribution

It provides a well-posedness result for evolutionary equations with fractional time-integrals and demonstrates its application to a Kelvin-Voigt type material model.

Findings

Proves well-posedness for fractional integral-based evolutionary equations

Applies the theoretical results to a Kelvin-Voigt type model

Enhances mathematical understanding of fractional material laws

Abstract

A well-posedness result for a time-shift invariant class of evolutionary operator equations involving material laws with fractional time-integrals of order $\alpha\in]0,1[$ is considered and exemplified by an application to a Kelvin-Voigt type model.