Abstract
The fractional-order differential equations that exist in the field of science and engineering have been studied in this paper. The 2D fluid flow problems are recommended for the classical- and fractional-order analysis. It has been found that the nonlinear fractional-order problems are more realistic than the classical models to describe the proposed flow problems since the behavior of the stress of the model problem is not linear. The similarity variable in this study has been used in fractional form to transform the modeled governing equations from partial PDEs. The acquired equations are the nonlinear ordinary differential equations (ODEs) in fractional form. The electromagnetic field has also been imposed into the fluid motion to calculate the embedded constraints in the case of classical and noninteger orders. The nonlinear problems are attempted using the FDE-12 technique. The important physical phenomena including Nusselt number and skin friction are also calculated in case of the integer- and noninteger-order problems. The electric and magnetic fields are examined and discussed in the case of fractional form and classical form.