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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.
Highlights
Mathematical models as routes of interpreting real-life situations are included in the literature
The wastewater model has been studied from a classical viewpoint and modelled by one of the most robust non-local fractional operators, called the Caputo operator
The dynamical features of the model were depicted through the steady-state region in its classical sense
Summary
Mathematical models as routes of interpreting real-life situations are included in the literature. These models display a vital update in the quantification and assessment of real-life problems and preventive measures [1,2,3]. Mathematical modeling has, in many ways, proven to be a very versatile and effective way of studying the dynamics of many situations. It is widely accepted that by using mathematical models, the prediction to control and solve real-life problems can be reached. A relevant argument here is that it is important to obtain acceptable criteria for the particular situation under consideration and to use these criteria to determine the effects of potential control measures. Several noteworthy attempts have recently been made to establish results through mathematical modelling [4,5,6,7,8]
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