The umbral operational techniques offer sturdy mechanism in the studies of special functions and special polynomials. The techniques of the umbral calculus are employed to derive the properties of families of exponential like functions and their hyperbolic forms. The generalized forms of Mittag-Leffler functions are used to solve the technical problems concerning the transport of a charged beam in a solenoid magnet. The proposed method is flexible and has many advantages over the standard computational techniques.