Generalized fractional free electron laser equations: pulse propagation and transverse mode cases

The present paper deals. with the fractional generalizations of a Volterra-type integro differential equation known as the Free Electron Laser equation. Here we solve the non- homogeneous forms of fractional free electron laser equations (FFEL) in two cases: pulse propagation and transverse mode. The solutions are obtained in closed forms in terms of the modified Kummer function phi* (alpha, beta; z) together with Hermite polynomials and Laguerre polynomials by the application of Riemann Liouville fractional integral operators.