Abstract
The main objective is to apply the concept of newly developed idea of the fractional-order derivative of the Rabotnov fractional-exponential function in fluid dynamics. In this article, a newly developed idea of the fractional-order derivative of the Rabotnov fractional-exponential function and the nonsingular kernel has been applied to study viscous fluid flow in the presence of an applied magnetic field. The flow is considered over an infinite vertical plate moving with arbitrary velocity. The modeled problem is transformed into a nondimensional form via dimensionless analysis, and then the Laplace transform method is applied for the solution of the problem. Due to the complexity in Laplace inversion, a strong numerical inversion procedure, namely, Zakian's algorithm, has been used, and the results are computed in various plots and tables. The corresponding discussion of results is included in detail. It is concluded that the generalized fractional-order derivative is accurate and efficient for describing general fractional-order dynamics in complex and power law phenomena.