Eur. Phys. J. Plus (2017) 132: 527
https://doi.org/10.1140/epjp/i2017-11798-7

Regular Article

Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

¹ Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico
² CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
³ Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico

^* e-mail: jgomez@cenidet.edu.mx

Received: 15 October 2017
Accepted: 14 November 2017
Published online: 18 December 2017

Abstract

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when , we recover the standard electrodynamics.