---
_id: '55607'
author:
- first_name: Khaled
  full_name: Hariz Belgacem, Khaled
  id: '98857'
  last_name: Hariz Belgacem
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  last_name: Ober-Blöbaum
- first_name: 'Fernando '
  full_name: 'Jiménez, Fernando '
  last_name: Jiménez
citation:
  ama: Hariz Belgacem K, Ober-Blöbaum S, Jiménez F. Fractional variational integrators
    based on convolution quadrature. Published online 2024.
  apa: Hariz Belgacem, K., Ober-Blöbaum, S., &#38; Jiménez, F. (2024). <i>Fractional
    variational integrators based on convolution quadrature</i>.
  bibtex: '@article{Hariz Belgacem_Ober-Blöbaum_Jiménez_2024, title={Fractional variational
    integrators based on convolution quadrature}, author={Hariz Belgacem, Khaled and
    Ober-Blöbaum, Sina and Jiménez, Fernando }, year={2024} }'
  chicago: Hariz Belgacem, Khaled, Sina Ober-Blöbaum, and Fernando  Jiménez. “Fractional
    Variational Integrators Based on Convolution Quadrature,” 2024.
  ieee: K. Hariz Belgacem, S. Ober-Blöbaum, and F. Jiménez, “Fractional variational
    integrators based on convolution quadrature.” 2024.
  mla: Hariz Belgacem, Khaled, et al. <i>Fractional Variational Integrators Based
    on Convolution Quadrature</i>. 2024.
  short: K. Hariz Belgacem, S. Ober-Blöbaum, F. Jiménez, (2024).
date_created: 2024-08-14T09:02:04Z
date_updated: 2024-08-14T09:14:49Z
ddc:
- '510'
file:
- access_level: closed
  content_type: application/pdf
  creator: hariz
  date_created: 2024-08-14T09:00:32Z
  date_updated: 2024-08-14T09:00:32Z
  file_id: '55608'
  file_name: 2403.18362v1.pdf
  file_size: 895203
  relation: main_file
  success: 1
file_date_updated: 2024-08-14T09:00:32Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2403.18362
oa: '1'
related_material:
  link:
  - relation: confirmation
    url: https://doi.org/10.48550/arXiv.2403.18362
status: public
title: Fractional variational integrators based on convolution quadrature
type: preprint
user_id: '98857'
year: '2024'
...
---
_id: '55605'
author:
- first_name: Khaled
  full_name: Hariz Belgacem, Khaled
  id: '98857'
  last_name: Hariz Belgacem
citation:
  ama: Hariz Belgacem K. <i>High-Order Embedding Formalism, Noether’s Theorem on Time
    Scales and Eringen’s Nonlocal Elastica</i>.; 2022.
  apa: Hariz Belgacem, K. (2022). <i>High-order embedding formalism, Noether’s theorem
    on time scales and Eringen’s nonlocal elastica</i>.
  bibtex: '@book{Hariz Belgacem_2022, title={High-order embedding formalism, Noether’s
    theorem on time scales and Eringen’s nonlocal elastica}, author={Hariz Belgacem,
    Khaled}, year={2022} }'
  chicago: Hariz Belgacem, Khaled. <i>High-Order Embedding Formalism, Noether’s Theorem
    on Time Scales and Eringen’s Nonlocal Elastica</i>, 2022.
  ieee: K. Hariz Belgacem, <i>High-order embedding formalism, Noether’s theorem on
    time scales and Eringen’s nonlocal elastica</i>. 2022.
  mla: Hariz Belgacem, Khaled. <i>High-Order Embedding Formalism, Noether’s Theorem
    on Time Scales and Eringen’s Nonlocal Elastica</i>. 2022.
  short: K. Hariz Belgacem, High-Order Embedding Formalism, Noether’s Theorem on Time
    Scales and Eringen’s Nonlocal Elastica, 2022.
date_created: 2024-08-14T08:53:38Z
date_updated: 2024-08-14T09:10:42Z
ddc:
- '510'
extern: '1'
file:
- access_level: open_access
  content_type: application/pdf
  creator: hariz
  date_created: 2024-08-14T08:53:31Z
  date_updated: 2024-08-14T08:53:31Z
  file_id: '55606'
  file_name: PhDThesis.pdf
  file_size: 4492215
  relation: main_file
file_date_updated: 2024-08-14T08:53:31Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- url: https://univ-pau.hal.science/tel-03776279v1
oa: '1'
related_material:
  link:
  - relation: confirmation
    url: https://univ-pau.hal.science/tel-03776279v1
status: public
title: High-order embedding formalism, Noether's theorem on time scales and Eringen's
  nonlocal elastica
type: dissertation
user_id: '98857'
year: '2022'
...
---
_id: '39400'
abstract:
- lang: eng
  text: <jats:p> The Eringen’s nonlocal elastica equation does not possess a Lagrangian
    formulation. In this article, we find a variational integrating factor which enables
    us to provide a Lagrangian and Hamiltonian structure associated to this equation.
    Explicit expressions of the solutions in terms of elliptic integrals of the first
    kind are then deduced. We then derive discrete version of the Eringen’s nonlocal
    elastica preserving the Lagrangian and Hamiltonian structure and compare it with
    Challamel’s and co-worker definition of a discrete Eringen’s nonlocal elastica.
    </jats:p>
article_number: '108128652211080'
author:
- first_name: Jacky
  full_name: Cresson, Jacky
  last_name: Cresson
- first_name: Khaled
  full_name: Hariz Belgacem, Khaled
  id: '98857'
  last_name: Hariz Belgacem
citation:
  ama: Cresson J, Hariz Belgacem K. About the structure of the discrete and continuous
    Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>. Published
    online 2022. doi:<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>
  apa: Cresson, J., &#38; Hariz Belgacem, K. (2022). About the structure of the discrete
    and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>,
    Article 108128652211080. <a href="https://doi.org/10.1177/10812865221108094">https://doi.org/10.1177/10812865221108094</a>
  bibtex: '@article{Cresson_Hariz Belgacem_2022, title={About the structure of the
    discrete and continuous Eringen’s nonlocal elastica}, DOI={<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>},
    number={108128652211080}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE
    Publications}, author={Cresson, Jacky and Hariz Belgacem, Khaled}, year={2022}
    }'
  chicago: Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the
    Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics
    of Solids</i>, 2022. <a href="https://doi.org/10.1177/10812865221108094">https://doi.org/10.1177/10812865221108094</a>.
  ieee: 'J. Cresson and K. Hariz Belgacem, “About the structure of the discrete and
    continuous Eringen’s nonlocal elastica,” <i>Mathematics and Mechanics of Solids</i>,
    Art. no. 108128652211080, 2022, doi: <a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>.'
  mla: Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the Discrete
    and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>,
    108128652211080, SAGE Publications, 2022, doi:<a href="https://doi.org/10.1177/10812865221108094">10.1177/10812865221108094</a>.
  short: J. Cresson, K. Hariz Belgacem, Mathematics and Mechanics of Solids (2022).
date_created: 2023-01-24T10:18:34Z
date_updated: 2023-08-01T11:52:17Z
doi: 10.1177/10812865221108094
keyword:
- Mechanics of Materials
- General Materials Science
- General Mathematics
language:
- iso: eng
publication: Mathematics and Mechanics of Solids
publication_identifier:
  issn:
  - 1081-2865
  - 1741-3028
publication_status: published
publisher: SAGE Publications
status: public
title: About the structure of the discrete and continuous Eringen’s nonlocal elastica
type: journal_article
user_id: '98857'
year: '2022'
...
---
_id: '39399'
article_number: '113502'
author:
- first_name: Baptiste
  full_name: Anerot, Baptiste
  last_name: Anerot
- first_name: Jacky
  full_name: Cresson, Jacky
  last_name: Cresson
- first_name: Khaled
  full_name: Hariz Belgacem, Khaled
  id: '98857'
  last_name: Hariz Belgacem
- first_name: Frederic
  full_name: Pierret, Frederic
  last_name: Pierret
citation:
  ama: Anerot B, Cresson J, Hariz Belgacem K, Pierret F. Noether’s-type theorems on
    time scales. <i>Journal of Mathematical Physics</i>. 2020;61(11). doi:<a href="https://doi.org/10.1063/1.5140201">10.1063/1.5140201</a>
  apa: Anerot, B., Cresson, J., Hariz Belgacem, K., &#38; Pierret, F. (2020). Noether’s-type
    theorems on time scales. <i>Journal of Mathematical Physics</i>, <i>61</i>(11),
    Article 113502. <a href="https://doi.org/10.1063/1.5140201">https://doi.org/10.1063/1.5140201</a>
  bibtex: '@article{Anerot_Cresson_Hariz Belgacem_Pierret_2020, title={Noether’s-type
    theorems on time scales}, volume={61}, DOI={<a href="https://doi.org/10.1063/1.5140201">10.1063/1.5140201</a>},
    number={11113502}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing},
    author={Anerot, Baptiste and Cresson, Jacky and Hariz Belgacem, Khaled and Pierret,
    Frederic}, year={2020} }'
  chicago: Anerot, Baptiste, Jacky Cresson, Khaled Hariz Belgacem, and Frederic Pierret.
    “Noether’s-Type Theorems on Time Scales.” <i>Journal of Mathematical Physics</i>
    61, no. 11 (2020). <a href="https://doi.org/10.1063/1.5140201">https://doi.org/10.1063/1.5140201</a>.
  ieee: 'B. Anerot, J. Cresson, K. Hariz Belgacem, and F. Pierret, “Noether’s-type
    theorems on time scales,” <i>Journal of Mathematical Physics</i>, vol. 61, no.
    11, Art. no. 113502, 2020, doi: <a href="https://doi.org/10.1063/1.5140201">10.1063/1.5140201</a>.'
  mla: Anerot, Baptiste, et al. “Noether’s-Type Theorems on Time Scales.” <i>Journal
    of Mathematical Physics</i>, vol. 61, no. 11, 113502, AIP Publishing, 2020, doi:<a
    href="https://doi.org/10.1063/1.5140201">10.1063/1.5140201</a>.
  short: B. Anerot, J. Cresson, K. Hariz Belgacem, F. Pierret, Journal of Mathematical
    Physics 61 (2020).
date_created: 2023-01-24T10:17:50Z
date_updated: 2023-08-01T11:51:51Z
doi: 10.1063/1.5140201
extern: '1'
intvolume: '        61'
issue: '11'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - 0022-2488
  - 1089-7658
publication_status: published
publisher: AIP Publishing
status: public
title: Noether’s-type theorems on time scales
type: journal_article
user_id: '98857'
volume: 61
year: '2020'
...