A Note on Fractional Evolutionary Equations

TL;DR

This paper investigates linear evolutionary equations with fractional derivatives, establishing well-posedness and causality, and illustrating applications in fractional Fokker-Planck equations and visco-elastic materials.

Contribution

It introduces a framework for fractional evolutionary equations, proving well-posedness and causality, and discusses initial condition imposition.

Findings

Proved well-posedness for fractional evolutionary equations

Established causality in the solution framework

Demonstrated applications to fractional Fokker-Planck and visco-elastic models

Abstract

A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a fractional Fokker-Planck type equation and a class of visco-elastic materials described via fractional derivatives. In conclusion the possibility of imposing initial conditions is discussed.