Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense

To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of micropollutants found in their influent streams is be...

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Autores principales:	Rubayyi T. Alqahtani, Shabir Ahmad, Ali Akgül
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Caputo operator Euler method functional analysis Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c015ec9e917247ab8b06e56cdf889102
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spelling	oai:doaj.org-article:c015ec9e917247ab8b06e56cdf8891022021-11-11T18:19:41ZMathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense10.3390/math92127872227-7390https://doaj.org/article/c015ec9e917247ab8b06e56cdf8891022021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2787https://doaj.org/toc/2227-7390To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of micropollutants found in their influent streams is becoming increasingly pressing. The removal of micropollutants in treatment plants is investigated using a model that incorporates biodegradation and sorption as the key processes of micropollutant removal. This article provides the mathematical analysis of the wastewater model that describes the removal of micropollutant in treatment plants under a non-local operator in Caputo sense. The positivity of the solution is presented for the Caputo fractional model. The steady state’s solution of model and their stability is presented. The fixed point theorems of Leray–Schauder and Banach are used to deduce results regarding the existence of the solution of the model. Ulam–Hyers (UH) types of stabilities are presented via functional analysis. The fractional Euler method is used to find the numerical results of the proposed model. The numerical results are illustrated via graphs to show the effects of recycle ratio and the impact of fractional order on the evolution of the model.Rubayyi T. AlqahtaniShabir AhmadAli AkgülMDPI AGarticleCaputo operatorEuler methodfunctional analysisMathematicsQA1-939ENMathematics, Vol 9, Iss 2787, p 2787 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Caputo operator Euler method functional analysis Mathematics QA1-939
spellingShingle	Caputo operator Euler method functional analysis Mathematics QA1-939 Rubayyi T. Alqahtani Shabir Ahmad Ali Akgül Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
description	To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of micropollutants found in their influent streams is becoming increasingly pressing. The removal of micropollutants in treatment plants is investigated using a model that incorporates biodegradation and sorption as the key processes of micropollutant removal. This article provides the mathematical analysis of the wastewater model that describes the removal of micropollutant in treatment plants under a non-local operator in Caputo sense. The positivity of the solution is presented for the Caputo fractional model. The steady state’s solution of model and their stability is presented. The fixed point theorems of Leray–Schauder and Banach are used to deduce results regarding the existence of the solution of the model. Ulam–Hyers (UH) types of stabilities are presented via functional analysis. The fractional Euler method is used to find the numerical results of the proposed model. The numerical results are illustrated via graphs to show the effects of recycle ratio and the impact of fractional order on the evolution of the model.
format	article
author	Rubayyi T. Alqahtani Shabir Ahmad Ali Akgül
author_facet	Rubayyi T. Alqahtani Shabir Ahmad Ali Akgül
author_sort	Rubayyi T. Alqahtani
title	Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
title_short	Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
title_full	Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
title_fullStr	Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
title_full_unstemmed	Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
title_sort	mathematical analysis of biodegradation model under nonlocal operator in caputo sense
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c015ec9e917247ab8b06e56cdf889102
work_keys_str_mv	AT rubayyitalqahtani mathematicalanalysisofbiodegradationmodelundernonlocaloperatorincaputosense AT shabirahmad mathematicalanalysisofbiodegradationmodelundernonlocaloperatorincaputosense AT aliakgul mathematicalanalysisofbiodegradationmodelundernonlocaloperatorincaputosense
_version_	1718431908613849088

Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense

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