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, p...
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doaj-29c527c087014550aec8d05787030a0c2020-11-25T04:03:17ZengElsevierJournal of Ocean Engineering and Science2468-01332020-12-0154310322Analysis of Lakes pollution model with Mittag-Leffler kernelD.G. Prakasha0P. Veeresha1Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere-577007, Karnataka, IndiaDepartment of Mathematics, Karnatak University, Dharwad-580003, Karnataka, India; Corresponding Author.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.http://www.sciencedirect.com/science/article/pii/S2468013320300127Lakes systemAtangana-Baleanu derivativeLaplace transformFixed point theoremq-Homotopy analysis method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
D.G. Prakasha P. Veeresha |
spellingShingle |
D.G. Prakasha P. Veeresha Analysis of Lakes pollution model with Mittag-Leffler kernel Journal of Ocean Engineering and Science Lakes system Atangana-Baleanu derivative Laplace transform Fixed point theorem q-Homotopy analysis method |
author_facet |
D.G. Prakasha P. Veeresha |
author_sort |
D.G. Prakasha |
title |
Analysis of Lakes pollution model with Mittag-Leffler kernel |
title_short |
Analysis of Lakes pollution model with Mittag-Leffler kernel |
title_full |
Analysis of Lakes pollution model with Mittag-Leffler kernel |
title_fullStr |
Analysis of Lakes pollution model with Mittag-Leffler kernel |
title_full_unstemmed |
Analysis of Lakes pollution model with Mittag-Leffler kernel |
title_sort |
analysis of lakes pollution model with mittag-leffler kernel |
publisher |
Elsevier |
series |
Journal of Ocean Engineering and Science |
issn |
2468-0133 |
publishDate |
2020-12-01 |
description |
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. |
topic |
Lakes system Atangana-Baleanu derivative Laplace transform Fixed point theorem q-Homotopy analysis method |
url |
http://www.sciencedirect.com/science/article/pii/S2468013320300127 |
work_keys_str_mv |
AT dgprakasha analysisoflakespollutionmodelwithmittaglefflerkernel AT pveeresha analysisoflakespollutionmodelwithmittaglefflerkernel |
_version_ |
1724440858116227072 |