Flow over an infinite plate of a viscous fluid with non-integer order derivative without singular kernel

Exact general solutions for the dynamics of an incompressible viscous fluid with non-integer order derivative without singular kernel are established using the integral transforms. These solutions, which are organized in simple forms in terms of exponential and trigonometric functions, can be conveniently engaged to obtain known solutions from the literature. The control of the new non-integer order derivative on the velocity of the fluid moreover a comparative study with an older model, is analyzed for some flows with practical applications. The non-integer order derivative with non-singular kernel is more appropriate for handling mathematical calculations of obtained solutions. It is also more reliable for numerical computations.