Over the last few years, the Mittag-Leffler function is drawn the attention of several special functionalist. In 21st century this is one of the frequently useful functions in the research area of Engineering, Technology and Applied Sciences. This book therefore provides a new generalization of Mittag-Leffler function, its related fractional operators and Decomposition (Chapters-2 & 3) with their various results. The new general class of polynomials by employing operational technique introduced in the Chapter-4 with their several properties and special cases. Chapter-5 concerns the generalizations of well-known Laguerre polynomials, Konhauser polynomials and a set of polynomials. Generating relations of these polynomials are connected with Mittag-Leffler and Wright functions. Integral representations of this new set of polynomials are also established. Chapter 6 deals with generalization of the instability phenomenon in fluid flow through porous media with mean capillary pressure by transforming the problem into Fractional partial differential equation and Mittag-Leffler function.