Second-grade fluid model with Caputo–Liouville generalized fractional derivative

In this paper, we propose a novel method for obtaining the solution of the fractional differential equation in the class of second-grade fluids models. The technique described in this paper is called the double integral method. The method generates, in general, an approximate solution for the fractional diffusion equations, the energy equations, or the heat equations. In our study, we use the generalized fractional derivative in Caputo–Liouville’s sense. For the illustrations of our method, we propose the graphical representations of the approximates solutions obtained by using the double integral method. We propose interpretations and physical discussions of the solutions obtained with the double integral method.