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General Fractional Calculus with Nonsingular Kernels: New Prospective on Viscoelasticity

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Methods of Mathematical Modelling and Computation for Complex Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 373))

Abstract

In the chapter, the general fractional derivatives in the different kernel functions, such as Mittag-Lefller, Wiman and Prabhakar functions are considered to model the viscoelastic behaviors in the real materials. We investigate the basic formulas of the fractional calculus (FC) in the kernels of the power, Mittag-Lefller, Wiman and Prabhakar functions. We discuss the applications for the general fractional calculus (GFC) in viscoelasticity. As the examples, the Maxwell and Voigt models with the general fractional derivatives (GFD) are considered to represent the complexity of the real materials.

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Acknowledgements

This work is supported by the State Key Research Development Program of the People’s Republic of China (Grant No.2016YFC0600705), the Natural Science Foundation of China (Grant No.51323004), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD2014).

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, XuzhouJiangsu, 221116, China

    Xiao-Jun Yang, Feng Gao & Yang Ju

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Xiao-Jun Yang & Feng Gao

  3. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology At Beijing, Beijing, 100083, China

    Yang Ju

Authors
  1. Xiao-Jun Yang
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Correspondence to Xiao-Jun Yang .

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Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

    Devendra Kumar

  4. Department of Mathematics and Computer Sciences, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  5. Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria

    Jordan Hristov

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Yang, XJ., Gao, F., Ju, Y. (2022). General Fractional Calculus with Nonsingular Kernels: New Prospective on Viscoelasticity. In: Singh, J., Dutta, H., Kumar, D., Baleanu, D., Hristov, J. (eds) Methods of Mathematical Modelling and Computation for Complex Systems. Studies in Systems, Decision and Control, vol 373. Springer, Cham. https://doi.org/10.1007/978-3-030-77169-0_6

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  • DOI: https://doi.org/10.1007/978-3-030-77169-0_6

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  • Online ISBN: 978-3-030-77169-0

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