Micro-plastic pollution is the major ultimatum to contaminate agricultural soils and empirical situation to lessening the soil quality and fertility. In this work the soil pollution due to ...micro-plastic in the Atangana-Baleanu-Caputo fractal dimension and fractional order inquiry with four compartments namely, Microplastic (P(t)), Soil pollution (S(t)), Remediate or recycling (R(t)) and Soil Nutrients cycle (N(t)). The qualitative analysis of the steady states is explained as locally stable, globally stable and Hyer Ulam stable. The expected equilibrium point appears in a pollution-free equilibrium point and pollution-extinct equilibrium point. Two significant best control strategies (u1(t) and u2(t)) are found to reduce soil pollution. Sensitivity analyses bring off the nature of various deportment of Basic reproduction numbers. Numerical approximation extracted with the help of Newton's Polynomial method. The purpose of precise expected results is demonstrated as a numerical simulation for various orders (0≤α≤0.6) and dimensions.
This study formulates a Monkeypox model with protected travelers. The fixed point theorem is used to obtain the existence and uniqueness of the solution with Ulam–Hyers stability for the analysis of ...the solution to the model. The Newton polynomial interpolation scheme is employed to solve an approximate solution of the fractional Monkeypox model. The numerical simulations and the graphical representations suggest that the fractional order affects the dynamics of the Monkeypox. The fractional order shows other underlining transmission trends of the Monkeypox disease. We conclude that the result obtained for each compartment conforms to reality as the fractional order approaches unity.
•This article formulates a fractional-order Monkeypox model with protected travelers.•The fixed-point theorem obtains the uniqueness, and the Ulam–Hyers stability criteria analyze the solution.•A basic reproduction number is obtained, and the local stability of the disease equilibrium point is analyzed.•The Newton polynomial interpolation finds an approximate solution for the fractional Monkeypox model.•The result for each compartment conforms to reality as the fractional order approaches unity.
•A piecewise COVID-19 is considered.•Dynamics of the proposed models are discussed.•Environmental noises are added to the model for the description in form of stochastic model.•Utilizing ...Caputo-Fabrizio fractional derivative operator for the purpose of constructing of the fractional-order model.•Numerically solved the proposed models.
In the current manuscript, we deal with the dynamics of a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model. For this, we discussed the deterministic, stochastic, and fractional forms of the proposed model for different steps. It has a great impact on the infectious disease models and especially for covid-19 because in start the deterministic model played its role but with time due to uncertainty the stochastic model takes place and with long term expansion the use of fractional derivatives are required. The stability of the model is discussed regarding the reproductive number. Using the non-standard finite difference scheme for the numerical solution of the deterministic model and illustrate the obtained results graphically. Further, environmental noises are added to the model for the description of the stochastic model. Then take out the existence and uniqueness of positive solution with extinction for infection. Finally, we utilize a new technique of piecewise differential and integral operators for approximating Caputo-Fabrizio fractional derivative operator for the purpose of constructing of the fractional-order model. Then study the dynamics of the models such as positivity and boundedness of the solutions and local stability analysis. Solved numerically fractional-order model used Newton Polynomial scheme and present the results graphically.
Fractional order and fractal order are mathematical tools that can be used to model real-world problems. In order to demonstrate the usefulness of these operators, we develop a new fractal-fractional ...model for the propagation of the Zika virus. This model includes insecticide-treated nets and the generalized fractal-fractional Mittag-Leffler kernel. The existence, uniqueness, and Ulam–Hyres stability conditions for the given system are determined. Using the Newton polynomial, the numerical scheme is described. From the numerical simulations, we notice that a change in the fractal-fractional order directly affects the dynamics of the Zika virus. We also notice that the use of fractal order only converges to faster than the use of fractional order only. Testing the inherent potency of insecticide-treated nets when the fractal-fractional order is 0.99 indicates that increased use of insecticide-treated nets increases the number of healthy humans. The fractal-fractional analysis captures the geometric pattern of the Zika virus that is repeated at every scale, which cannot be captured by classical geometry. This backs up the idea that the best way to control the disease is to know enough about how it spread in the past.
•A new fractal-fractional Zika epidemic model with Mittag-Leffler kernel is proposed.•Ulam–Hyres condition for the given system is determined using nonlinear functional analysis.•The Newton interpolation is used to obtain the numerical solution.•Memory effects and repeated patterns are presented.
In this study, we present new numerical scheme for modified Chua attractor model with fractional operators. However we give numerical solution of the considered model with fractal-fractional ...operators. Also, we offer error analysis for a general Cauchy problem with fractional and fractal-fractional operators. For numerical solution of the considered equation, we use new numerical scheme which is established with an efficient polynomial known as Newton interpolation polynomial. The results are discussed with some examples and simulations.
In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, ...bifurcations, Lyapunov exponent, phase portraits, Poincaré mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).
This study aims to explore the intricate and concealed chaotic structures of meminductor systems and their applications in applied sciences by utilizing fractal fractional operators (FFOs).
The ...dynamical analysis of a three-dimensional meminductor system with FFO in the Caputo sense is presented, and a unique solution for the system is obtained via a novel contraction in an orbitally complete metric space. Numerical results are derived using a newly developed method based on Newton polynomial. The analysis includes variations in fractional order and fractal dimension, with a presentation of properties such as Lyapunov spectra, bifurcations, Poincar’e sections, attractor projection, inversion property, and time series analysis.
The numerical simulations uncovered intricate hidden attractors for certain values of fractional and fractal orders. This study provides insight into the effects of FFOs on analyzing hidden chaotic attractors and presents a novel approach to understanding and analyzing the dynamics of meminductor systems. The study’s findings contribute to the understanding of the complex and hidden structures of meminductor systems using FFOs. The novel method developed in this study could be applied to other dynamical systems, leading to further advancements in the analysis of complex systems.
•A meminductor system with sinusoidal source is considered.•Generalized nonlocal operators are used.•Some dynamical features are studied.•Using MATLAB software, hidden attractors are analyzed.
There are many fatal diseases which are caused by virus. Different types of viruses cause different infections. One of them is HIV-1 infection which caused by retrovirus. HIV-1 infection is a ...hazardous disease that can lead to cancer, AIDS, and other serious illnesses. Several mathematical models have been proposed in the field and examined using various methods. In this manuscript, the newly suggested piece-wise (PW) Atangana–Baleanu (AB) fractional operator is used to examine HIV-1 infection. Some theorems related to the existence of the solution to the examined model are proved through fixed point results. The Ulam–Hyers (UH) stability and its different forms are presented for the proposed PW HIV-1 infection model. The considered model’s numerical results are attained via the Newton interpolation method. The results are graphically illustrated via MATLAB software to show the behavior of the considered model. Oscillatory and complex dynamics are obtained for some fractional orders and show the crossover behavior of the proposed model. The model’s simulation of infected class is fitted with the real data taken for six different countries. It proves the validity and accuracy of the suggested approach.
This paper proposes a new fractal–fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo–Fabrizio fractional order derivative. Caputo–Fabrizio fractal–fractional order is ...particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal–fractional order is varied.
The newly arose irresistible sickness known as the Covid illness (COVID-19), is a highly infectious viral disease. This disease caused millions of tainted cases internationally and still represent a ...disturbing circumstance for the human lives. As of late, numerous mathematical compartmental models have been considered to even more likely comprehend the Covid illness. The greater part of these models depends on integer-order derivatives which cannot catch the fading memory and crossover behavior found in many biological phenomena. Along these lines, the Covid illness in this paper is studied by investigating the elements of COVID-19 contamination utilizing the non-integer Atangana–Baleanu–Caputo derivative. Using the fixed-point approach, the existence and uniqueness of the integral of the fractional model for COVID is further deliberated. Along with Ulam–Hyers stability analysis, for the given model, all basic properties are studied. Furthermore, numerical simulations are performed using Newton polynomial and Adams Bashforth approaches for determining the impact of parameters change on the dynamical behavior of the systems.
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