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

被引：14

作者：

Alqahtani, Rubayyi T. ^{[1
]}

Yusuf, Abdullahi ^{[2
,3
]}

Agarwal, Ravi P. ^{[4
]}

机构：

[1] Al Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh 11566, Saudi Arabia

[2] Biruni Univ, Dept Comp Engn, TR-34010 Istanbul, Turkey

[3] Fed Univ Dutse, Dept Math, Jigawa 7156, Nigeria

[4] Texas A M Univ, Dept Math, Kingsville, TX 78363 USA

来源：

MATHEMATICS | 2021年 / 9卷 / 06期

关键词：

wastewater model; stability analysis; Caputo fractional operator; existense and uniqueness results; numerical dynamics; FRACTIONAL DERIVATIVES; MASS-TRANSFER; MODEL; EPIDEMIC; DISEASE; FLOW;

D O I：

10.3390/math9060675

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：19

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