Fractional Approach for Equation Describing the Water Transport in Unsaturated Porous Media With Mittag-Leffler Kernel

In this paper, we find the solution for a fractional Richards equation describing the water transport in unsaturated porous media using the q-homotopy analysis transform method (q-HATM). The proposed technique is to use graceful amalgamations of the Laplace transform technique with the q-homotopy analysis scheme as well as the fractional derivative that is defined with the Atangana-Baleanu (AB) operator. The fixed point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to validate and illustrate the efficiency of the future technique, we analyze the projected model in terms of fractional order. Meanwhile, the physical behavior of the q-HATM solutions are captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The achieved results illuminate that the future algorithm is easy to implement, highly methodical, effective, and very accurate in its analysis of the behavior of non-linear differential equations of fractional order that arise in the connected areas of science and engineering.