Fractional Free Electron Laser Equation and K-Function

Abstract

Abstract

In this era, fractional free electron laser (FEL) equations are studied due to their utility and importance in mathematical physics and engineering. The aim of present paper is to find the solution of generalized fractional order free electron laser (FEL) equation, using K-function. The results obtained here are moderately universal in nature. Special cases, relating to the exponential function are also considered. The special functions were introduced in 18th century to define solutions of differential equations emerging as mathematical models of certain problems in astronomy, physics and biological science. The adjective ‘special’ of this nomenclature can be attributed to the simple fact that these functions owed their origin to special circumstances. Here we present a brief survey of the hypergeometric functions and their generalized forms due to the prime importance of hypergeometric functions in the study of special functions.

Keywords: Fractional free electron laser (FEL) equation, K-function, generalized M-series, Riemann-Liouville operator

Cite this Article

Manoj Sharma, Kishan Sharma. Fractional Free Electron Laser Equation and K-Function. Research & Reviews: Discrete Mathematical Structures. 2017; 4(2): 17–20p.