Fractional derivatives, memory kernels and solution of a free electron laser Volterra type equation
type: Item
instance of: scholarly article
title: Fractional derivatives, memory kernels and solution of a free electron laser Volterra type equation
zbMATH Open document ID: 1394.45006
author: Marcello Artioli
author: G. Dattoli
author: Silvia Licciardi
author: Simonetta Pagnutti
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 6898702
zbMATH Keywords: free electron laser (FEL)
zbMATH Keywords: iterative solutions
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: Legendre polynomials
MaRDI profile type: Publication
full work available at URL: math5040073
OpenAlex ID: W2775686030
cites work: Q5190149
cites work: Fractional rheological models for thermomechanical systems. Dissipation and free energies
cites work: DISSIPATIVITY AND IRREVERSIBILITY OF ELECTROMAGNETIC SYSTEMS
DOI: 10.3390/MATH5040073
description: scientific article; zbMATH DE number 6898702