Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20497 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916923015430144 |
|---|---|
| author | Pathak, Shashank Ruzhansky, Michael Van Bockstal, Karel |
| author_facet | Pathak, Shashank Ruzhansky, Michael Van Bockstal, Karel |
| contents | We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $β\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate Mittag-Leffler function consisting of a double infinite series. Although this series is uniformly convergent, its numerical implementation suffers from computational instabilities. In this contribution, we propose an approximate closed-form solution that avoids these numerical pitfalls while maintaining a reasonable accuracy. The resulting approximation is computationally efficient and robust, making it suitable for practical engineering applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators Pathak, Shashank Ruzhansky, Michael Van Bockstal, Karel Classical Analysis and ODEs Mathematical Physics 34A08, 70J35, 74S40 We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $β\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate Mittag-Leffler function consisting of a double infinite series. Although this series is uniformly convergent, its numerical implementation suffers from computational instabilities. In this contribution, we propose an approximate closed-form solution that avoids these numerical pitfalls while maintaining a reasonable accuracy. The resulting approximation is computationally efficient and robust, making it suitable for practical engineering applications. |
| title | A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators |
| topic | Classical Analysis and ODEs Mathematical Physics 34A08, 70J35, 74S40 |
| url | https://arxiv.org/abs/2508.20497 |