ABSTRACT
The present chapter considers the applications of the special functions in describing the exact analytical solutions of a class of fluid models described by the fractional operators. In the present investigations, the Caputo derivative has been used as an operator. The special functions used in the present chapter are the exponential function, the Mittag-Leffler function, the Gaussian error function, the Bessel function, and others. In the modeling, a fractional operator has been considered, we have used the Caputo derivative fractional operator. The findings of the chapter have been illustrated by several graphical representations, and the impact of the parameters used in the modeling of the fluid dynamics and the influence of the fractional operator have been analyzed and interpreted in detail. The physical theories to justify the behaviors of the dynamics of the considered fluid have been provided.
