Moving front solutions of a time-fractional power-law fluid under gravity

Abstract

This paper considers a fractional-order, incompressible power-law fluid on a horizontal plane, where the time component is defined by Riemann-Liouville derivatives. The model is characterized by a nonlinear second-order partial differential equation comprising of a power-law parameter β. We transform the model into nonlinear fractional ordinary differential equations and subsequently, solutions of the latter are determined analytically. In the case of a Newtonian fluid, we show that moving front solutions are obtained irrespective of the presence of fractional derivatives. Graphical representations for the moving front solutions are presented. Lastly, we find a nonclassical solution for the integer-order power-law fluid model.