Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative

Rubayyi T. Alqahtani, Abdullahi Yusuf and Ravi P. Agarwal
Additional contact information
Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia
Abdullahi Yusuf: Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
Ravi P. Agarwal: Department of Mathematics, Texas A M University-Kingsville, Kingsville, TX 78363, USA

Mathematics, 2021, vol. 9, issue 6, 1-19

Abstract: In this paper, the wastewater treatment model is investigated by means of one of the most robust fractional derivatives, namely, the Caputo fractional derivative. The growth rate is assumed to obey the Contois model, which is often used to model the growth of biomass in wastewaters. The characteristics of the model under consideration are derived and evaluated, such as equilibrium, stability analysis, and steady-state solutions. Further, important characteristics of the fractional wastewater model allow us to understand the dynamics of the model in detail. To this end, we discuss several important analyses of the fractional variant of the model under consideration. To observe the efficiency of the non-local fractional differential operator of Caputo over its counter-classical version, we perform numerical simulations.

Keywords: wastewater model; stability analysis; Caputo fractional operator; existense and uniqueness results; numerical dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/6/675/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/6/675/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:6:p:675-:d:521642

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().