New similarity variable to transform the fluid flow from PDEs into fractional-order ODEs: Numerical study

Abstract

The recent research aims to study the fractional-order differential equations of the higher-order. The problems consist of momentum and thermal boundary layers. The similarity variables are introduced to convert the partial differential equations (PDEs) into the fractional-order ordinary differential equations (ODEs). The two nonlinear problems of fractional order ODEs are tackled through the (Fractional Differential equation-12) FDE-12 method. The obtained results show that the fractional-order problems are more nonlinear as compared to the integer-order differential equations. The fractional-order increasing the nonlinearity and consequently more efforts required to obtain the outputs. The impact of the physical parameters in the case of the integer-order and fractional-order are obtained and discussed. It is observed that the impact of the physical parameters more compact in the case of fractional order as compared to the integer-order case. The important features of the drag force and heat transfer rate in the case of the fractional-order boundary value problem also have been analyzed and discussed.