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

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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).

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Acknowledgements

Authors would like to thankful to all the anonymous reviewers for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, IIIT, Kota, MNIT Campus, Jaipur, Rajasthan, 302017, India

    Priyanka Harjule

  2. Department of Applied Sciences, Engineering College, Banswara, Rajasthan, 327001, India

    Manish Kumar Bansal

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  1. Priyanka Harjule
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  2. Manish Kumar Bansal
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Correspondence to Manish Kumar Bansal.

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Harjule, P., Bansal, M.K. Fractional Order Models for Viscoelasticity in Lung Tissues with Power, Exponential and Mittag–Leffler Memories. Int. J. Appl. Comput. Math 6, 119 (2020). https://doi.org/10.1007/s40819-020-00872-9

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