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

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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 \( \alpha = 1\), we recover the standard electrodynamics.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico

    V. F. Morales-Delgado

  2. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

  3. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico

    M. A. Taneco-Hernandez

Authors
  1. V. F. Morales-Delgado
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  2. J. F. Gómez-Aguilar
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  3. M. A. Taneco-Hernandez
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Correspondence to J. F. Gómez-Aguilar.

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Morales-Delgado, V.F., Gómez-Aguilar, J.F. & Taneco-Hernandez, M.A. Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives. Eur. Phys. J. Plus 132, 527 (2017). https://doi.org/10.1140/epjp/i2017-11798-7

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