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Energy dissipation for hereditary and energy conservation for non-local fractional wave equations

Dusan Zorica and Ljubica Oparnica (UGent)
(2020) PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 378(2172).
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Abstract
Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
Keywords
General Engineering, General Physics and Astronomy, General Mathematics, VISCOELASTIC MEDIA, MICROLOCAL ANALYSIS, CREEP, PROPAGATION, ATTENUATION, MODEL, fractional wave equation, hereditary and non-local fractional, constitutive equations, energy dissipation and conservation

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MLA
Zorica, Dusan, and Ljubica Oparnica. “Energy Dissipation for Hereditary and Energy Conservation for Non-Local Fractional Wave Equations.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 378, no. 2172, 2020, doi:10.1098/rsta.2019.0295.
APA
Zorica, D., & Oparnica, L. (2020). Energy dissipation for hereditary and energy conservation for non-local fractional wave equations. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 378(2172). https://doi.org/10.1098/rsta.2019.0295
Chicago author-date
Zorica, Dusan, and Ljubica Oparnica. 2020. “Energy Dissipation for Hereditary and Energy Conservation for Non-Local Fractional Wave Equations.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 378 (2172). https://doi.org/10.1098/rsta.2019.0295.
Chicago author-date (all authors)
Zorica, Dusan, and Ljubica Oparnica. 2020. “Energy Dissipation for Hereditary and Energy Conservation for Non-Local Fractional Wave Equations.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 378 (2172). doi:10.1098/rsta.2019.0295.
Vancouver
1.
Zorica D, Oparnica L. Energy dissipation for hereditary and energy conservation for non-local fractional wave equations. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 2020;378(2172).
IEEE
[1]
D. Zorica and L. Oparnica, “Energy dissipation for hereditary and energy conservation for non-local fractional wave equations,” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 378, no. 2172, 2020.
@article{8669431,
  abstract     = {{Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.}},
  articleno    = {{20190295}},
  author       = {{Zorica, Dusan and Oparnica, Ljubica}},
  issn         = {{1364-503X}},
  journal      = {{PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}},
  keywords     = {{General Engineering,General Physics and Astronomy,General Mathematics,VISCOELASTIC MEDIA,MICROLOCAL ANALYSIS,CREEP,PROPAGATION,ATTENUATION,MODEL,fractional wave equation,hereditary and non-local fractional,constitutive equations,energy dissipation and conservation}},
  language     = {{eng}},
  number       = {{2172}},
  pages        = {{24}},
  title        = {{Energy dissipation for hereditary and energy conservation for non-local fractional wave equations}},
  url          = {{http://doi.org/10.1098/rsta.2019.0295}},
  volume       = {{378}},
  year         = {{2020}},
}
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