Abstract
In this paper, an approximate similarity solution of a fractional laminar boundary layer of viscous fluid flow over an infinite vertical plate has been presented. We introduce new fractional similarity transformations to convert the partial differential equation into a similarity ordinary differential equation with a fractional context. The viscous term of the flow momentum equation is written based on the Caputo fractional derivative. The proposed analytical solution has been developed using fractional power-series technique, and the convergence of the solution has been examined. The velocity distributions with the similarity variable are plotted against different values of the fractional order to illustrate the effects of fractional argument on the velocity behavior.