Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

V.F. Morales-Delgado, J.F. Gómez-Aguilar, R.F. Escobar-Jiménez and M.A. Taneco-Hernández

Physica A: Statistical Mechanics and its Applications, 2018, vol. 503, issue C, 424-438

Abstract: This paper presents a novel fractional conformable derivative of Liouville–Caputo type of fractional order α=n−ϵ that contains a small ϵ and positive integer n values between [1;2]. The method is applied to obtain analytical solutions for the electrical circuits LC and RL and for the equations that describe the motion of a charged particle in an electromagnetic field using an expansion of the fractional conformable derivative in ϵ=n−α. Numerical simulations were obtained for different values of the fractional order and the parameter ϵ. This novel fractional conformable derivative allows describing physical systems where the level of fractality is low, such as oscillators, quantum dynamics, electromagnetic fields, mechanics of fractal and complex media, among others.

Keywords: Fractional calculus; Low-fractality; Electrical circuits; Fractional conformable derivative (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437118303261
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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:eee:phsmap:v:503:y:2018:i:c:p:424-438

DOI: 10.1016/j.physa.2018.03.018

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().