Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense

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dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.contributor.authorAlqahtani, Rubayyi T.
dc.contributor.authorAhmad, Shabir
dc.contributor.authorAkguel, Ali
dc.date.accessioned2024-12-24T19:33:42Z
dc.date.available2024-12-24T19:33:42Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractTo 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.
dc.description.sponsorshipDeanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University
dc.description.sponsorshipThe APC was funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University.
dc.identifier.doi10.3390/math9212787
dc.identifier.issn2227-7390
dc.identifier.issue21
dc.identifier.scopus2-s2.0-85118773005
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math9212787
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8244
dc.identifier.volume9
dc.identifier.wosWOS:000720463700001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectCaputo operator
dc.subjectEuler method
dc.subjectfunctional analysis
dc.titleMathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
dc.typeArticle

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