Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense

Abstract

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.

Bright Soliton Behaviours of Fractal Fractional Nonlinear Good Boussinesq Equation with Nonsingular Kernels

“…These operators have many applications in different fields of science. For instance, fractional operators have been used in analysis of biodegradation modeling [15], biomath [16], mathematical physics [17,18], and engineering [19,20].…”

Adaptive Technique for Solving 1-D Interface Problems of Fractional Order

“…Riemann–Liouville and Caputo were the first to investigate the generalization of ordinary integral and differential operators into fractional derivatives. The fractional-order differential equations offer a logical framework for studying real-world problems such as Rubella disease modal [ 12 ], waste water modal [ 13 ], economic growth model [ 14 ], diffusion processes [ 15 ], coronavirus disease and Covid-19 models sense [ 16 , 17 ], in [ 18 ] the authors solve the system of nonlinear fractional order PDEs involving of power law kernel using hybrid analytical technique. On the other hand there is some work on a new method for solving fractional PDEs in [ 19 ].…”