Distributed-order time-fractional wave equations
- Author
- Frederik Broucke (UGent) and Ljubica Oparnica (UGent)
- Organization
- Project
- Abstract
- Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the distributed-order constitutive law. In this work, we propose to take positive Radon measures for the constitutive “functions.” First, we derive a thermodynamical restriction on the constitutive measures which is easy to check and therefore suitable for applications. Then, we prove that the setting with measures in combination with the derived thermodynamical restriction guarantees existence and uniqueness of solutions for the distributed-order fractional wave equation. We further discuss the support and regularity of the fundamental solution and conclude with a discussion on wave velocities.
- Keywords
- Fractional wave equation, Distributed-order fractional derivative, Constitutive equation, Positive Radon measures, Wave speed, MODEL
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01GPAVP392EPHGAJ6V935MTEX7
- MLA
- Broucke, Frederik, and Ljubica Oparnica. “Distributed-Order Time-Fractional Wave Equations.” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 74, no. 1, 2023, doi:10.1007/s00033-022-01899-2.
- APA
- Broucke, F., & Oparnica, L. (2023). Distributed-order time-fractional wave equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 74(1). https://doi.org/10.1007/s00033-022-01899-2
- Chicago author-date
- Broucke, Frederik, and Ljubica Oparnica. 2023. “Distributed-Order Time-Fractional Wave Equations.” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 74 (1). https://doi.org/10.1007/s00033-022-01899-2.
- Chicago author-date (all authors)
- Broucke, Frederik, and Ljubica Oparnica. 2023. “Distributed-Order Time-Fractional Wave Equations.” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 74 (1). doi:10.1007/s00033-022-01899-2.
- Vancouver
- 1.Broucke F, Oparnica L. Distributed-order time-fractional wave equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. 2023;74(1).
- IEEE
- [1]F. Broucke and L. Oparnica, “Distributed-order time-fractional wave equations,” ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, vol. 74, no. 1, 2023.
@article{01GPAVP392EPHGAJ6V935MTEX7,
abstract = {{Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the distributed-order constitutive law. In this work, we propose to take positive Radon measures for the constitutive “functions.” First, we derive a thermodynamical restriction on the constitutive measures which is easy to check and therefore suitable for applications. Then, we prove that the setting with measures in combination with the derived thermodynamical restriction guarantees existence and uniqueness of solutions for the distributed-order fractional wave equation. We further discuss the support and regularity of the fundamental solution and conclude with a discussion on wave velocities.}},
articleno = {{19}},
author = {{Broucke, Frederik and Oparnica, Ljubica}},
issn = {{0044-2275}},
journal = {{ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}},
keywords = {{Fractional wave equation,Distributed-order fractional derivative,Constitutive equation,Positive Radon measures,Wave speed,MODEL}},
language = {{eng}},
number = {{1}},
pages = {{25}},
title = {{Distributed-order time-fractional wave equations}},
url = {{http://doi.org/10.1007/s00033-022-01899-2}},
volume = {{74}},
year = {{2023}},
}
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