A fractional model of fluid flow through porous media with mean capillary pressure

In this paper, we discuss a fractional model arising in flow of two incompatible liquids through homogenous porous media with mean capillary pressure. The solution is derived by the application of the Sumudu transform and the Fourier sine transform. The results are received in compact and graceful forms in terms of the generalized Mittag-Leffler function, which are suitable for numerical computation. The mathematical formulation leads to generalized fractional derivative which has been solved by using a numerical technique by employing the iterative process with the help of appropriate boundary conditions. This problem has great importance in petroleum technology.