On a generalized fractional integro-differential equation of Volterra-type

The following fractional generalization of the free electron laser (FEL) equation is studied: D-tau(alpha)(tau) = lambda (tau)integral(0) t(delta)alpha(tau - t)e(ivt)dt + beta e(iv tau), 0 less than or equal to r less than or equal to 1, where beta, lambda epsilon C epsilon R, and delta > -1. An analytical treatment of this fractional integral equation leads to a closed form solution in terms of Kummer functions Phi (a, b; x). The solution is also expressed in terms of incomplete gamma functions gamma*(a,x). Finally, Tau method approximation is used in the numerical evaluation of the results. MSC (1991): 26A33, 33C15.