Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator

Jessica Mendiola-Fuentes (), Eugenio Guerrero-Ruiz and Juan Rosales-García
Additional contact information
Jessica Mendiola-Fuentes: Departamento de Ciencias Básicas e Ingenierías, Universidad del Caribe, L-1. Mz 1, Esq. Fracc. Tabachines SM 78, Cancún 77528, Quintana Roo, Mexico
Eugenio Guerrero-Ruiz: Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico, Rio Piedras Campus, 17 Ave. Universidad Suite 1701, San Juan 00925-2537, Puerto Rico
Juan Rosales-García: Departamento de Ingeniería Eléctrica, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, km. 3.5 + 1.8 km, Comunidad Palo Blanco, Salamanca 36885, Guanajuato, Mexico

Mathematics, 2024, vol. 12, issue 10, 1-11

Abstract: The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of a more diverse array of behaviors. Furthermore, if the effect of the fractional derivative is applied to each of the terms of the differential equation, this will involve greater complexity in the description of the analytical solutions of the fractional differential equation. In this work, by using the Laplace method, the solutions to the multiple-term forced fractional harmonic oscillator are presented, described through multivariate Mittag-Leffler functions. Additionally, the cases of damped and undamped free fractional harmonic oscillators are addressed. Finally, through simulations, the effect of the fractional non-integer derivative is demonstrated, and the consistency of the result is verified when recovering the integer case.

Keywords: fractional forced oscillator; multivariate Mittag-Leffler function; fractional calculus; multivariate Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/10/1502/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/10/1502/ (text/html)

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:gam:jmathe:v:12:y:2024:i:10:p:1502-:d:1392784

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().