Novel fractional differential operator and its application in fluid dynamics

Abstract

Theoretical analysis of unsteady incompressible viscous fluid has been carried with constant proportional Caputo fractional derivative namely constant proportional Caputo type with singular kernel. The modeled considered in this paper is the fundament problem of fluid dynamics. The resulting governing equations are modeled with hybrid fractional operator of singular kernel and its solution obtained by using Laplace transform method and expressed in terms of series. Some graphs are captured for fractional parameter αα for large and small time and found that velocity shows dual trend for small and large values of time for different values of fractional parameter $\alpha$. Further, compared the present results with the results obtained with new fractional operators and found that constant proportional Caputo type operator portrait better velocity decay. Moreover, for increasing time, momentum boundary layer thickness increases while for grater values of fractional parameter it reduces.