(1)Analysis of Lakes pollution model with Mittag-Leffler kernel
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D.G. Prakasha a, P. Veeresha b,∗
a Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere-577007, Karnataka, India
b Department of Mathematics, Karnatak University, Dharwad-580003, Karnataka, India
Received 10 December 2019; received in revised form 16 January 2020; accepted 17 January 2020
Available online 6 February 2020
Abstract
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.
© 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/)
Keywords: Lakes system; Atangana-Baleanu derivative; Laplace transform; Fixed point theorem; q-Homotopy analysis method.