Mathematical modeling for adsorption process of dye removal nonlinear equation using power law and exponentially decaying kernels

Abstract

In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo–Fabrizio, and the Atangana–Baleanu–Caputo with the fractional parameter χ, where 0<χ≤1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model’s solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained.

Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator

“…where f 1 , g 1 and k 1 are the functions obtained by the inverse Laplace transform in (30). In a similar manner, we reach…”

“…It can be predicted that in the future, a definition covering all definitions of fractional operators available in the literature may be introduced. To learn more about the content of this study, we refer the readers to [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19

“…Such system can be very difficult to model and analyze with classical differential equations, but non – locality gives fractional derivative built-in ability to incorporate memory effects [11] . Fractional differential equations appear naturally in numerous fields of study including physics, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electrodynamics of complex medium, viscoelasticity, capacitor theory, electrical circuits, electron-analytical chemistry, biology, control theory, and fitting of experimental data [ [12] , [13] , [14] , [23] , [24] , [25] , [26] ]. Recently there are many studies on epidemiological disease modeling using fractional order differential equations [27] , [28] , [29] , [30] , [31] , [32] , [33] .…”

The Impact of the SARS-CoV-2 Epidemic on World Indices: The Entropy Approach

“…Besides, Hashemi et al [20] used the Adams-Bashforth-Moulton scheme (ABMS) to determine the approximate solution of a variable-order fractional three-dimensional chaotic process, demonstrating simulation results. However, Qureshi [21] examined a new timeinvariant nonlinear mathematical model in fractional-(noninteger-) order settings that has been proposed under the three most frequently employed strategies of the classical Caputo. Currently, all world stock markets have been affected by the virus.…”