Fractional Order Models for Viscoelasticity in Lung Tissues with Power, Exponential and Mittag–Leffler Memories

Abstract

Various models on Viscoelasticity have been used to comprehend mechanics of lung tissues in a better way. In this paper we present efficient mathematical framework using new and modified fractional derivatives to model the viscoelasticity in lung tissues. We demonstrate that replacing the time derivatives by fractionary-order derivatives in the constitutional expression of classical spring-dashpot system instinctively gives rise to power-law relaxation function and continuous-period impedance. Application of fractionary-order time derivative involving non-local as well as non-singular kernel is presented. Results obtained in this paper can be closely compared to the results obtained by Craiem et al. (Phys Med Biol 53:4543–4554, 2008).