An Application of Fractional Calculus to Column Theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909667947446272 |
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| author | Villa-Morales, José Ramírez-Aranda, Manuel |
| author_facet | Villa-Morales, José Ramírez-Aranda, Manuel |
| contents | In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the fractional parameter, there exists a critical buckling force. Additionally, we provide a numerical scheme for accurately approximating this critical force. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Application of Fractional Calculus to Column Theory Villa-Morales, José Ramírez-Aranda, Manuel General Mathematics 34A12, 34A08, 74B05, 74A10 In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the fractional parameter, there exists a critical buckling force. Additionally, we provide a numerical scheme for accurately approximating this critical force. |
| title | An Application of Fractional Calculus to Column Theory |
| topic | General Mathematics 34A12, 34A08, 74B05, 74A10 |
| url | https://arxiv.org/abs/2507.00021 |