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Linear and Nonlinear Fractional Voigt Models

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear case, an explicit Volterra representation of the solution is found, involving the generalized Mittag-Leffler function in the kernel. For the nonlinear fractional Voigt model, an existence result is obtained through a fixed point theorem. A nonlinear example, illustrating the obtained existence result, is given.

This work is part of first author’s Ph.D., which is carried out at Houari Boumediene University, Algeria.

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Acknowledgments

This research was finished while Chidouh was visiting University of Aveiro, Portugal. The hospitality of the host institution and the financial support of Houari Boumedienne University, Algeria, are here gratefully acknowledged. Torres was supported by CIDMA and FCT within project UID/MAT/04106/2013. The authors are grateful to two referees for valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Laboratory of Dynamic Systems, Houari Boumediene University, Algiers, Algeria

    Amar Chidouh & Rachid Bebbouchi

  2. Laboratory of Advanced Materials, Badji Mokhtar-Annaba University, Annaba, Algeria

    Assia Guezane-Lakoud

  3. Laboratory of Industrial Mechanics, Badji Mokhtar-Annaba University, Annaba, Algeria

    Amor Bouaricha

  4. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

Authors
  1. Amar Chidouh
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  2. Assia Guezane-Lakoud
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  3. Rachid Bebbouchi
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  4. Amor Bouaricha
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  5. Delfim F. M. Torres
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Corresponding author

Correspondence to Delfim F. M. Torres .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Chidouh, A., Guezane-Lakoud, A., Bebbouchi, R., Bouaricha, A., Torres, D.F.M. (2017). Linear and Nonlinear Fractional Voigt Models. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

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