On certain fractional calculus operators and applications in mathematical physics

In this paper, we modify the (k, s) fractional integral operator involving k-Mittag-Leffler function and discuss its properties. We originate a new fractional operator named (k, s)-Prabhakar derivative and obtained some classical fractional operators as a special case of the newly proposed derivative. Some properties of the introduced operator are also part of the present work. The generalized Laplace transform is employed to study the characteristics of fractional operators. We modeled the free-electron laser (FEL) equation by involving the proposed derivative and can find the solution by using the said Laplace transform. (paper)