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Maxwell's equations and electromagnetic Lagrangian density in fractional form

### Abstract

The fractional form of the electromagneticLagrangian density is presented using the Riemann-Liouville fractional derivative. Agrawal procedure is employed to obtain Maxwell's equations in fractional form. The Hamilton equations of motion resulting from the electromagneticLagrangian density are obtained. Conserved quantities, such as energy density, momentum, and Poynting's vector, are also derived using fractional Noether's theorem.

© 2012 American Institute of Physics

Received 22 January 2011
Accepted 18 November 2011
Published online 12 March 2012

Article outline:

I. INTRODUCTION
II. BASIC MATHEMATICAL DEFINITION
III. FRACTIONAL ELECTROMAGNETICLAGRANGIAN DENSITY
IV. FRACTIONAL HAMILTONIAN FORMULATION (LRLFD)
V. NOETHER’S THEOREM IN FRACTIONAL FORM
VI. CONCLUSION

/content/aip/journal/jmp/53/3/10.1063/1.3670375

http://aip.metastore.ingenta.com/content/aip/journal/jmp/53/3/10.1063/1.3670375

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