A computational study of vibrating system using the constant proportional Caputo derivative operator approach

Azhar Ali Zafar (), Muhammad Armaghan Sadiq (), Khurram Shabbir () and Liliana Guran
Additional contact information
Azhar Ali Zafar: Department of Mathematics, Government College University, Lahore 54000, Pakistan
Muhammad Armaghan Sadiq: Department of Mathematics, Government College University, Lahore 54000, Pakistan
Khurram Shabbir: Department of Mathematics, Government College University, Lahore 54000, Pakistan
Liliana Guran: Department of Hospitality Services, BabeÅŸ-Bolyai University, Cluj-Napoca 400174, Romania

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 05, 1-31

Abstract: For modeling of complex systems, in signal processing, and the explorations of nonlinear dynamics and memory effects, the utilization of noninteger-order dynamics provides adaptable control over oscillation patterns and frequencies. Moreover, various waveforms result in unique sonic qualities. By manipulation of these waveforms, musicians and sound designers have the capacity to craft a wide spectrum of auditory experiences, ranging from basic tones to intricate sound scape. This paper is about study of such vibrating systems using the noninteger-order derivative operator approach. In particular, we will discuss fractional relaxation oscillator and Scott-Blair oscillator employing constant proportional Caputo fractional derivative operator. Laplace transform method and Tzou’s numerical inversion algorithm are utilized to solve these vibrating models with respective initial conditions. A thorough graphical analysis is done to discuss the control of noninteger-order parameters and the parameters involved in the definition of fractional derivative operator. Finally, useful conclusions are recorded to highlight the behavior of oscillators and influence of noninteger-order parameters, the parameters involved in the definition of fractional derivative operator and system parameters that are helpful in controlling over oscillation pattern, frequencies and shape of vibrations produced by the vibrating systems.

Keywords: Vibrating systems; constant proportional Caputo derivative operator; Laplace transform (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183124502310
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:36:y:2025:i:05:n:s0129183124502310

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183124502310

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().