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Fractional Derivatives, Memory Kernels and Solution of a Free Electron Laser Volterra Type Equation

Author

Listed:
  • Marcello Artioli

    (ENEA—Bologna Research Center, Via Martiri di Monte Sole, 4, 40129 Bologna, Italy)

  • Giuseppe Dattoli

    (ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy)

  • Silvia Licciardi

    (ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
    Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6, 95125 Catania, Italy)

  • Simonetta Pagnutti

    (ENEA—Bologna Research Center, Via Martiri di Monte Sole, 4, 40129 Bologna, Italy)

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.

Suggested Citation

  • Marcello Artioli & Giuseppe Dattoli & Silvia Licciardi & Simonetta Pagnutti, 2017. "Fractional Derivatives, Memory Kernels and Solution of a Free Electron Laser Volterra Type Equation," Mathematics, MDPI, vol. 5(4), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:73-:d:121464
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    Citations

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    Cited by:

    1. Alexander Iomin, 2022. "Koopman Operator and Path Integral of Quantum Free-Electron Laser Model," Mathematics, MDPI, vol. 10(21), pages 1-14, October.

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