Fractional derivatives, memory kernels and solution of a free electron laser volterra type equation

Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi, Simonetta Pagnutti

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Abstract

The high gain free electron laser (FEL) equation is a Volterra type integro-differential equation amenable for analytical solutions in a limited number of cases. In this note, a novel technique, based on an expansion employing a family of two variable Hermite polynomials, is shown to provide straightforward analytical solutions for cases hardly solvable with conventional means. The possibility of extending the method by the use of expansion using different polynomials (two variable Legendre like) expansion is also discussed.
Original languageEnglish
Article number73
Pages (from-to)-
JournalMathematics
Volume5
Issue number4
DOIs
Publication statusPublished - 4 Dec 2017
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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