{"type":"journal_article","issue":"2","date_updated":"2025-02-24T11:55:58Z","_id":"58811","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\n          <jats:p>Fractional dissipation is a powerful tool to study nonlocal physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational formulation of the model. In Jiménez and Ober-Blöbaum (J Nonlinear Sci 31:46, 2021), a new approach is proposed to deal with dissipative systems including fractionally damped systems in a variational way for both, the continuous and discrete setting. It is based on the doubling of variables and their fractional derivatives. The aim of this work is to derive higher-order fractional variational integrators by means of convolution quadrature (CQ) based on backward difference formulas. We then provide numerical methods that are of order 2 improving a previous result in Jiménez and Ober-Blöbaum (J Nonlinear Sci 31:46, 2021). The convergence properties of the fractional variational integrators and saturation effects due to the approximation of the fractional derivatives by CQ are studied numerically.</jats:p>"}],"publication_identifier":{"issn":["0938-8974","1432-1467"]},"publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Khaled","last_name":"Hariz Belgacem","full_name":"Hariz Belgacem, Khaled"},{"full_name":"Jiménez, Fernando","last_name":"Jiménez","first_name":"Fernando"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"intvolume":"        35","status":"public","date_created":"2025-02-24T11:52:16Z","title":"Fractional Variational Integrators Based on Convolution Quadrature","volume":35,"article_number":"38","year":"2025","doi":"10.1007/s00332-025-10131-0","publication":"Journal of Nonlinear Science","language":[{"iso":"eng"}],"user_id":"98857","citation":{"short":"K. Hariz Belgacem, F. Jiménez, S. Ober-Blöbaum, Journal of Nonlinear Science 35 (2025).","bibtex":"@article{Hariz Belgacem_Jiménez_Ober-Blöbaum_2025, title={Fractional Variational Integrators Based on Convolution Quadrature}, volume={35}, DOI={<a href=\"https://doi.org/10.1007/s00332-025-10131-0\">10.1007/s00332-025-10131-0</a>}, number={238}, journal={Journal of Nonlinear Science}, publisher={Springer Science and Business Media LLC}, author={Hariz Belgacem, Khaled and Jiménez, Fernando and Ober-Blöbaum, Sina}, year={2025} }","apa":"Hariz Belgacem, K., Jiménez, F., &#38; Ober-Blöbaum, S. (2025). Fractional Variational Integrators Based on Convolution Quadrature. <i>Journal of Nonlinear Science</i>, <i>35</i>(2), Article 38. <a href=\"https://doi.org/10.1007/s00332-025-10131-0\">https://doi.org/10.1007/s00332-025-10131-0</a>","chicago":"Hariz Belgacem, Khaled, Fernando Jiménez, and Sina Ober-Blöbaum. “Fractional Variational Integrators Based on Convolution Quadrature.” <i>Journal of Nonlinear Science</i> 35, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00332-025-10131-0\">https://doi.org/10.1007/s00332-025-10131-0</a>.","mla":"Hariz Belgacem, Khaled, et al. “Fractional Variational Integrators Based on Convolution Quadrature.” <i>Journal of Nonlinear Science</i>, vol. 35, no. 2, 38, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00332-025-10131-0\">10.1007/s00332-025-10131-0</a>.","ama":"Hariz Belgacem K, Jiménez F, Ober-Blöbaum S. Fractional Variational Integrators Based on Convolution Quadrature. <i>Journal of Nonlinear Science</i>. 2025;35(2). doi:<a href=\"https://doi.org/10.1007/s00332-025-10131-0\">10.1007/s00332-025-10131-0</a>","ieee":"K. Hariz Belgacem, F. Jiménez, and S. Ober-Blöbaum, “Fractional Variational Integrators Based on Convolution Quadrature,” <i>Journal of Nonlinear Science</i>, vol. 35, no. 2, Art. no. 38, 2025, doi: <a href=\"https://doi.org/10.1007/s00332-025-10131-0\">10.1007/s00332-025-10131-0</a>."},"publication_status":"published"}