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arXiv · 2508.20497

A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators

Shashank Pathak·Michael Ruzhansky·Karel Van Bockstal
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Abstract

We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $\beta\in (0,1).$ 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.

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Shashank Pathak, Michael Ruzhansky, Karel Van Bockstal. 2025-08-28. A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators. https://doi.org/10.1016/j.jsv.2026.120019

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