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

Mathematics

Simonetta Pagnutti¹  Marcello Artioli¹  Giuseppe Dattoli²  Silvia Licciardi² 

[1] ENEA—Bologna Research Center, Via Martiri di Monte Sole, 4, 40129 Bologna, Italy;ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy;

关键词: free electron laser (FEL);    Volterra equations;    iterative solutions;    Hermite polynomials;    Legendre polynomials;   

DOI  :  10.3390/math5040073

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown