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Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys.53, 033505 (2012)]

### Abstract

In a recent paper, Jaradat et al. [J. Math. Phys.53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl.272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr.72, 119 (2005)].

© 2014 AIP Publishing LLC

Received 30 April 2013
Accepted 01 March 2014
Published online 13 March 2014

/content/aip/journal/jmp/55/3/10.1063/1.4868479

4.

4. P. A. M. Dirac, Lectures on Quantum Mechanics (Dover Publications Inc., Minola, NY, 1964).

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2014-03-13

2016-10-24

### Abstract

In a recent paper, Jaradat et al. [J. Math. Phys.53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl.272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr.72, 119 (2005)].

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