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For:
Piovella N
, Volpe L.
A Review of High-Gain Free-Electron Laser Theory.
Atoms
2021;
9
:28. [DOI:
10.3390/atoms9020028
]
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[Indexed: 12/15/2022]
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Fox H-Functions in Self-Consistent Description of a Free-Electron Laser.
FRACTAL AND FRACTIONAL
2021. [DOI:
10.3390/fractalfract5040263
]
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[Indexed: 11/16/2022]
Abstract
A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is the Laplace image of the kernel of the integro-differential equation, which is also known as a fractional FEL equation with Caputo–Fabrizio type fractional derivative. Asymptotic solutions of the equation are analyzed as well.
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