The following fractional generalization of the free electron laser equation is investigated:D τ α h(τ)=λ∫ 0 τ t δ h(τ-t)Φ(b;δ+1;iνt)dt+μτ γ Φ(β ,γ+1;iντ),0=<τ=<1,where β,γ,λ C; ν,b,β R, α>0, γ>-1 and δ>-1. A closed form solution is derived in terms of Kummer's function Φ(α,β;z) by the application of Riemann-Liouville fractional integration operators. Tau method approximation is used in the evaluation of the results in a suitable form for numerical computation. The results derived are of general character and provide extension of the work reported by Boyadjiev et al. and Al-Shammery et al. [Math. Comput. Model. 25 (1997) 1; Integral Transform. Spec. Funct. 9 (2000) 81; J. Fract. Cal. Appl. Anal. 2 (1999) 501].