In recent year’s fractional free electron laser (FEL) equation are studied due to their usefulness and importance in mathematical physics, The aim of present paper is to find the solution of generalized fractional order free electron laser (FEL) equation, using Mittag-Leffler special function. The results obtained here is moderately universal in nature. Special cases, relating to the exponential function is also considered.
In present paper, we have derived the fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit  and Sharma and Jain . As a special case, of fractional q-differentiation of Robotnov and Hartley’s function has been obtained.