Analysis of Lakes pollution model with Mittag-Leffler kernel

The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q homotopy analysis transform method (q-HATM). We consider three different cases of the considered model namely, periodic input model, exponentially decaying input model, and linear input model. The considered scheme is unifications of q-homotopy analysis technique with Laplace transform (LT). To illustrate the existence and uniqueness for the projected model, we consider the fixed point hypothesis. More preciously, we scrutinized the behaviour of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems. (c) 2020 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)