Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators

Abstract: Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators ; volume:56 ; number:1 ; year:2023 ; extent:15 ; Demonstratio mathematica ; 56, Heft 1 (2023) (gesamt 15)

Contributors, Places and Time

• Creator: Alharthi, Nadiyah Hussain ; Atangana, Abdon ; Alkahtani, Badr S.

Further information

• DOI: 10.1515/dema-2022-0230
• URN: urn:nbn:de:101:1-2023063014041289303436
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:45 AM CEST