International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 9, Issue 9 (September 2022), Pages: 25-32

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 Original Research Paper

 Fractional solution of helical motion of a charged particle under the influence of Lorentz force

 Author(s): Moaz Mohammad Altarawneh *

 Affiliation(s):

 Department of Physics, Mutah University, Mutah, Jordan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0001-9278-9907

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2022.09.004

 Abstract:

In this study, a generalized solution for the helical motion of a charged particle in uniform electric and magnetic fields is obtained using a powerful fractional derivative approach. Using this approach, the differential equations that describe the helical motion of a charged particle in the fields were obtained. The solution for the fractional differential equations is presented in great detail in terms of a series solution using the Mittag-Leffler function. The Laplace transform technique was used to solve the differential equations in the regular form and in the fractional form (with fractional parameter γ). Two and three-dimensional plots were presented for the trajectory of the particle before and after introducing the fractional operator for different values of γ. Features of delay in the motion and dissipation in the medium have been observed in the fractional solution too. The importance of our work stems from the two- and three-dimensional visualization of the obtained generalized helical trajectories that can be applied to similar types of motions in nature and the universe.

 © 2022 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Helical trajectory, Fractional operator, Laplace transform, Generalized solution, Mittag-Leffler function

 Article History: Received 7 March 2022, Received in revised form 22 May 2022, Accepted 31 May 2022

 Acknowledgment 

This work was supported by the deanship of scientific research at Mutah University.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Altarawneh MM (2022). Fractional solution of helical motion of a charged particle under the influence of Lorentz force. International Journal of Advanced and Applied Sciences, 9(9): 25-32

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 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4

 Tables

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