On a fractional generalization of the free electron laser equation

  • Authors:

  • R. K. Saxena;S. L. Kalla

  • Affiliations:

  • Department of Mathematics and Statistics, Jal Narain Vyas University, Jodhpur 342001, India;Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2003

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Abstract

The following fractional generalization of the free electron laser equation is investigated: Dταh(τ)= λ ∫0τ tδh(τ-t)Φ(b; δ + 1; ivt)dt + µτγΦ (β,γ+1;ivτ), 0 ≤ τ ≤ 1, where β,γ,λ ∈ C; v,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].