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arXiv · 1312.6019

Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications

Roberto Garra·Enzo Orsingher·Federico Polito
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Abstract

In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to a fractional hyper-Bessel-type equation. We find an exact analytic solution by using the McBride theory of fractional powers of hyper-Bessel operators. A discussion of these results within the framework of linear dispersive wave equations is provided. We also present exact solutions of the fractional Klein-Gordon equation in the higher dimensional cases. Finally, we suggest a method of finding travelling wave solutions of the nonlinear fractional Klein-Gordon equation with power law nonlinearities.

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Roberto Garra, Enzo Orsingher, Federico Polito. 2014-04-09. Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications. https://doi.org/10.1109/icfda.2014.6967381

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