Fractional relaxation model with general memory effects and stability analysis

Abstract

Voigt and Maxwell models are popularly used to model viscoelastic materials’ property. They are often presented in form of fractional relaxation equations. In order to describe rich viscoelasticity, a general Caputo derivative is introduced in fractional modeling. Then this work studies attractivity and asymptotic stability of the Caputo fractional relaxation equation with general memory effects. Firstly, the considered problem is transformed into an integral equation. A mapping and an attractive set are constructed. Furthermore, the existence of fixed points on the attractive set are investigated by using fixed point theorems. Finally, the effectiveness and convenience of the stability theory are verified through two numerical examples.