Laplace Adomian Decomposition Method Research Articles

Mathematical Evaluation and Dynamic Transmissions of a Tumor Growth Model Using a Generalized Singular and Non-Local Kernel

Currently, fractional calculus plays a critical role in improving control techniques, analyzing disease transmission dynamics, and solving several other real-world problems. This research investigates the time-fractional tumor growth model using an innovative approach. The new modified fractional derivative operator employs a singular and non-local kernel, based on Atangana and Baleanu's concepts with the Caputo derivative. The tumor growth model used the newly modified fractional operator, which provided numerical simulation. With the introduction of this new operator, we provide significant analysis for the tumor growth epidemic model. We have proven the uniqueness and stability conditions of the model by utilizing Banach's fixed point theory and the Picard successive approximation method. Using the Laplace-Adomian decomposition method (LADM), we found the numerical solution to the Modified Atangana-Baleanu-Caputo derivative model. We have verified the convergence analysis of the suggested scheme. We ultimately utilize the suggested method to obtain numeric outcomes and simulations for the tumor growth model. The study investigates the effect of multiple biological variables on the transmission of tumor growth dynamics.

Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space

This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer's fixed-point theorem, the Banach contraction theorem and the Arzel\`{a}-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman's inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both linear and non-linear FVFIDEs. The method's efficiency is demonstrated through some numerical examples.

Computational and numerical analysis of the fractional three-components nonlinear Schrödinger equation with singular and non-singular kernels

This work offer a computational approach to the coupled nonlinear Shrödinger equation (CNLSE) by utilizing fractional operators and double Laplace Adomian decomposition method (DLTADM). Three various fractional operators i.e Caputo, Caputo–Fabrizio (CF) and Atangana–Baleanu Caputo (ABC) are used for studying the approximate solution of the CNLSE. Dynamics of solutions are provided via graphical examples that depict system behavior. Graphs of the deduced results portray dark soliton dynamics for various fractional values. The robustness of the applied approach is studied via comparative analysis of error estimations between exact and derived results via tables and 2D graphs.

Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques

Abstract Monkeypox is a highly infectious disease and spreads very easily, hence posing several health concerns or risks as it may lead to outbreak. This article proposes a new mathematical model to simulate the transmission rate of the monkeypox virus-infected fractional-order differential equations using the Caputo–Fabrizio derivative. The existence, uniqueness, and stability under contraction mapping of the fixed point of the model are discussed using Krasnoselskii’s and Banach’s fixed point theorems. To verify the model proposed, we employ data that record the actual dynamics, and based on these data, the model can capture the observed transmission patterns in Ghana. Also, the analytic algorithm is used to find the result applying the Laplace Adomian decomposition method (LADM). Performance analysis of LADM is made regarding Runge-Kutta fourth order, which is the most commonly employed method for solving second-order ordinary differential equations. This comparison therefore offers information on the truth and reliability of the two techniques toward modeling the transmission pattern of the monkey pox virus. The information obtained through this study provides a better understanding of the antibodies linked to monkeypox virus spreading and provides effective strategies to doctors and politicians. This article helps shape better strategies about combating the impact of monkeypox virus in public health since it makes it easy to predict and prevent the occurrence of the disease.

Analytical investigation of convective phenomena with nonlinearity characteristics in nanostratified liquid film above an inclined extended sheet

Abstract This work focuses on the time-variant convective thin-film nanoliquid fluid flow and heat transfer over a stretching, inclined surface under the effect of magnetism for different energy technologies for sustainability. It is crucial to understand how solid materials can be treated with thin films while focusing on the actual ability to improve the body surface features for infiltration, shock resistance, rigidness, brightness, dispersal, absorption, or electrical efficiency. All of these improvements are invaluable, especially in the field of nanotechnology. As with any mass and thermal transport phenomena, the study breaks down important factors such as thermophoresis and Brownian movement, in an attempt to improve the energetic balance and lessen fuel consumption. Utilizing the mathematical model of the temporal evolution on the liquid film flow characteristics over an inclined surface, we obtain a system of nonlinear partial differential equations and convert it to a system of coupled ordinary differential equations appropriately. Finally, the results of the model problem computational analysis are produced using the Laplace Adomian decomposition method (LADM) and are shown both quantitatively and visually. During the flow analysis, the impact of specific flow parameters such as the magnetic, Brownian, and thermophoresis parameters are examined and found to be highly significant. Furthermore, it is found that the effects of ( M M ) and (Nt) factors on ( F F ), ( Φ \Phi ), and ( ϕ \phi ) lead to decreased conduction. Conversely, the thermal gradient within the liquid films rises in proportion to the (Nb) factor. This research is distinguished from similar attempts made in the past in terms of thin-film nanoliquid flow from inclined planes and application of LADM approach toward modeling. The findings have provided tangible use in coming up with new methods of cooling electronics gadgets, energy harvesting for solar energy, and eco-friendly industrial processes.

Fractional Order and Numerical Solution Application of Modeling in the Management of Examination Misconducts

The fractional order model that represents the spread of Examination misconduct using compartments of the population of honest students (susceptible), those lightly involved in misconduct (exposed), seriously involved ones (infected), and quitters (removed) is provided. The fractional order derivative is considered in the Caputo sense. To determine the epidemic forecast and persistence, we calculate the reproduction number. Analyzing the stability of this scheme ensures a non-negative and unique solution within the defined domain (0,1). Employing the Laplace-Adomian Decomposition Method aids in estimating the solution for the nonlinear fractional differential equations. Utilizing infinite series helps derive solutions for these equations, ensuring convergence to their precise values. The results obtained align with outcomes from the traditional Differential Transformed Method. Finally, numerical results and an outstanding graphic simulation are presented.

The Analysis of a Co-Dynamic Ebola and Malaria Transmission Model Using the Laplace Adomian Decomposition Method with Caputo Fractional-Order

The Analysis of a Co-Dynamic Ebola and Malaria Transmission Model Using the Laplace Adomian Decomposition Method with Caputo Fractional-Order

Analysis of Two Hybrid Schemes to Solve the Benjamin-Bona-Mahony (BBM) Equation

In this research, we compare and contrast two numerical methods, the Laplace Adomian Decomposition Method (LADM) and the Elzaki Projected Differential Transform Method (EPDTM), for solving the Benjamin-Bona-Mahony (BBM) equation, and this helps in evaluating their performance, assessing robustness, gaining insights into solution behavior, validating results, generalizing their applicability, and advancing the field. This rigorous comparisons validates the efficacy of the methods as we compare the exact results and the results of LADM and EPDTM, plotting the convergent of the two methods to identify the method that is highly convergent and accurate. Results identify the Elzaki Projected Differential Transform Method (EPDTM) as having a simple and accurate numerical method for solving the BBM equation. EPDTM enhances accessibility, computational efficiency, accuracy, robustness, and validation of the solutions, supporting the understanding and analysis of wave phenomena described by the BBM equation. This study contributes to the advancement of the field of numerical analysis and computational science as practical applications of BBM equation in various fields, including coastal engineering, wave modeling, and wave stability analysis cannot be over emphasize.

Analysis of two hybrid schemes to solve the Benjamin-Bona-Mahony (BBM) equation

In this research, we compare and contrast two numerical methods, the Laplace Adomian Decomposition Method (LADM) and the Elzaki Projected Differential Transform Method (EPDTM), for solving the Benjamin-Bona-Mahony (BBM) equation, and this helps in evaluating their performance, assessing robustness, gaining insights into solution behavior, validating results, generalizing their applicability, and advancing the field. This rigorous comparisons validates the efficacy of the methods as we compare the exact results and the results of LADM and EPDTM, plotting the convergent of the two methods to identify the method that is highly convergent and accurate. Results identify the Elzaki Projected Differential Transform Method (EPDTM) as having a simple and accurate numerical method for solving the BBM equation. EPDTM enhances accessibility, computational efficiency, accuracy, robustness, and validation of the solutions, supporting the understanding and analysis of wave phenomena described by the BBM equation. This study contributes to the advancement of the field of numerical analysis and computational science as practical applications of BBM equation in various fields, including coastal engineering, wave modeling, and wave stability analysis cannot be over emphasize.

Analysis of Caputo Fractional-Order Co-Infection COVID-19 and Influenza SEIR Epidemiology by Laplace Adomian Decomposition Method

Around the world, the people are simultaneously susceptible to or infected with several infections. This work aims at the analysis of the dynamics of transmission of two deadly viruses, COVID-19 and Influenza, using a co-infection epidemiological model by applying the Caputo fractional derivative. Fractional differential equations are currently used worldwide to model physical and biological phenomena. Our comprehension of complicated phenomena is improved when fractional-order derivatives are used to model systems with memory effects and long-range interactions. Mathematical depictions of infectious disease dynamics and dissemination across communities are provided by epidemiological models, which are essential resources for understanding and controlling infectious diseases. These models support informed decision making to prevent outbreaks, evaluate intervention measures, and help researchers and policymakers understand how diseases spread. A subclass of epidemiological models called co-infection models focuses on studying the dynamics of several infectious illnesses that occur in the same population at the same time. They are especially useful in situations where people are simultaneously susceptible to or infected with several infections. Co-infection models provide information on the development of effective control techniques, the progression of disease, and the interactions between several pathogens. The qualitative study via stability analysis is discussed at equilibrium, the reproduction number is computed, and the results are simulated using the Laplace Adomian Decomposition Method (LADM) for Fractional Differential Equations. We employ MATLAB R2023a for graphical presentations and numerical simulations.

Mathematical modeling of chickenpox transmission using the Laplace Adomian Decomposition Method

In this work, mathematical modeling of a nonlinear differential equation was studied to investigate the effect of vaccination on the spread of chickenpox. The proof of existence and uniqueness of the positive solution and invariant region showed that the model is epidemiologically sound. We established the disease-free and endemic equilibrium states and carried out a stability analysis of the disease-free and endemic equilibrium states of the model to gain insight into the dynamics of the model. The rate of vaccination and precaution for the spread of chickenpox was a factor that influenced the basic reproductive number, which was calculated using the next-generation matrix approach. Forecasts made via numerical simulation using the Laplace Adomian Decomposition method highlight the temporal impact of vaccination on curbing the chicken pox trend.

Analyzing co-infection dynamics: A mathematical approach using fractional order modeling and Laplace-Adomian decomposition

The co-infection of HIV and COVID-19 is a pressing health concern, carrying substantial potential consequences. This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 co-infection, a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches. Here, we introduce an innovative mathematical model grounded in Caputo fractional order differential equations, specifically designed to encapsulate the intricate dynamics of co-infection. This model encompasses multiple critical facets: the transmission dynamics of both HIV and COVID-19, the host’s immune responses, and the influence of treatment interventions. Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics. To tackle the fractional order model, we employ the Laplace-Adomian decomposition method, a potent mathematical tool for approximating solutions in fractional order differential equations. Utilizing this technique, we simulate the intricate interactions between these variables, yielding profound insights into the propagation of co-infection. Notably, we identify pivotal contributors to its advancement. In addition, we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method. This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions. Our findings hold significant implications for the formulation of effective control strategies. Policymakers, healthcare professionals, and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection.

Application of Laplace Adomian decomposition method for fractional Fokker-Planck equation and time fractional coupled Boussinesq-Burger equations

PurposeFractional Fokker-Planck equation (FFPE) and time fractional coupled Boussinesq-Burger equations (TFCBBEs) play important roles in the fields of solute transport, fluid dynamics, respectively. Although there are many methods for solving the approximate solution, simple and effective methods are more preferred. This paper aims to utilize Laplace Adomian decomposition method (LADM) to construct approximate solutions for these two types of equations and gives some examples of numerical calculations, which can prove the validity of LADM by comparing the error between the calculated results and the exact solution.Design/methodology/approachThis paper analyzes and investigates the time-space fractional partial differential equations based on the LADM method in the sense of Caputo fractional derivative, which is a combination of the Laplace transform and the Adomian decomposition method. LADM method was first proposed by Khuri in 2001. Many partial differential equations which can describe the physical phenomena are solved by applying LADM and it has been used extensively to solve approximate solutions of partial differential and fractional partial differential equations.FindingsThis paper obtained an approximate solution to the FFPE and TFCBBEs by using the LADM. A number of numerical examples and graphs are used to compare the errors between the results and the exact solutions. The results show that LADM is a simple and effective mathematical technique to construct the approximate solutions of nonlinear time-space fractional equations in this work.Originality/valueThis paper verifies the effectiveness of this method by using the LADM to solve the FFPE and TFCBBEs. In addition, these two equations are very meaningful, and this paper will be helpful in the study of atmospheric diffusion, shallow water waves and other areas. And this paper also generalizes the drift and diffusion terms of the FFPE equation to the general form, which provides a great convenience for our future studies.

The analytical analysis of fractional differential system via different operators and normalization functions

This article is related to the utilization of the Laplace Adomian Decomposition Method (LADM) to analyze the solution of a fractional order system under different operators and normalized functions. In this connection, the three new and updated operators i.e., Caputo, Caputo–Fabrizio, and Atangana–Baleano are used to define the fractional order derivative with the help of four different normalization functions. It is observed that, among the four normalized functions, the fourth kind of normalized function is the most suitable function for the above-mentioned operators. The LADM series solutions are obtained for both integer and fractional orders, implying that the proposed approach has a greater accuracy and convergence rate. Figures and Tables are constructed to verify the validity and efficiency of the suggested technique. LADM simulations confirmed, that the more iterations of LADM reduced the associated absolute error. Moreover, fractional order solutions are obtained which are convergent towards integer order solutions.

The analysis of a novel COVID-19 model with the fractional-order incorporating the impact of the vaccination campaign in Nigeria via the Laplace-Adomian Decomposition Method

This study underscores the crucial role of COVID-19 vaccinations in managing the pandemic, with a specific focus on Nigeria. Employing a fractional-order mathematical modeling approach, the research assesses vaccination efficacy, minimum effectiveness, and duration. The model’s numerical solution is derived through the Laplace Adomian Decomposition Method (LADM), utilizing rapidly converging infinite series. Simulation results illustrate the impact of COVID-19 transmission and vaccination rates. The study concludes that implementing a vaccination strategy in an integer order proves to be the most effective approach to controlling the spread of COVID-19. These findings have significant implications for researchers, policymakers, and healthcare workers. They emphasize the central role of fractional calculus in facilitating vaccine implementation in the ongoing battle against COVID-19. The study calls for global efforts to maximize vaccination implementation for the overall benefit of public health.

Modeling and dynamics of measles via fractional differential operator of singular and non-singular kernels

Young children frequently die from measles, which is a major global health concern. Despite being more prevalent in infants, pregnant women, and people with compromised immune systems, it can infect anyone. Novel fractional operators, the constant-proportional Caputo operator, and the constant-proportional Atangana–Baleanu operator are used to create a hybrid fractional order model that helps analyze the dynamic transmission of the measles virus. We assess the measles-free and endemic equilibrium, reproductive number, biological viability, boundedness, well-posedness, and positivity of the model. We apply the Banach contraction principle to verify the uniqueness of the system’s solutions. The proposed system is confirmed to be Ulam–Hyres stable by using fixed point theory results. The aforementioned operators are further analyzed, and the Laplace-Adomian decomposition method is used to numerically simulate the system of fractional differential equations. To support our findings, the outcomes are graphically displayed. The efficacy and memory impact of fractional operators are illustrated through comparisons. Based on fractional parameter values, the study determines important disease-control strategies and shows that vaccinations greatly reduce the spread of measles. By reducing the number of infected people, increasing vaccination coverage lowers the burden of disease on the general population.

Approximate Solution of the Fractional Order Mathematical Model on the Transmission Dynamics on The Co-Infection of COVID-19 and Monkeypox Using the Laplace-Adomian Decomposition Method

A fractional order compartmental model on the transmission dynamics of the co-infection of COVID-19 and Monkeypox is presented. The approximate solutions of the fractional order model are obtained using the Laplace-Adomian Decomposition method in the form of an infinite series which was shown to converge to the exact value. Using the MATLAB fmincon algorithm, we carried out a data fitting analysis using real life COVID-19 and Monkeypox data so as to obtain estimates for some of the key parameters used in the formulation of model. The results of our analysis showed that an increase in the effective treatment capacity in the human population will significantly reduce the burden of these diseases in the human population.

Approximate Solution of Fractional Order of Partial Differential Equations Using Laplace-Adomian Decomposition Method in MATLAB

This article presents the application of the Laplace-Adomian Decomposition Method (LADM) for solving partial differential equations (PDEs) in the context of heat conduction and wave propagation. The LADM combines Laplace transform and Adomian decomposition to approximate solutions to PDEs efficiently in MATLAB. The procedure involves transforming the PDE into simpler differential equations, which are then solved iteratively using the Adomian decomposition method. The advantages of LADM include simplicity, flexibility, and applicability to a wide range of PDEs. We demonstrate the effectiveness of LADM through numerical experiments solving the heat equation and wave equation using MATLAB. The results show good agreement with analytical solutions and highlight the efficiency and accuracy of LADM for solving PDEs.

Analysis of a mathematical model with hybrid fractional derivatives under different kernel for hearing loss due to mumps virus

ABSTRACT Genetics, birth defects, some viral diseases, persistent ear infections, medications, loud noises, and age can all cause hearing loss, a global health issue. The mumps are typically the cause of unilaterally acquired sensorineural hearing loss in children. A hybrid fractional operator model employing Constant Proportional Caputo (CPC), Constant Proportional Caputo Fabrizio (CPCF), and Constant Proportional Atangana-Baleanu Caputo (CPABC) in the Caputo sense is developed to investigate mumps induced hearing loss in children. We focused on the region that is positively invariant and well-posed in the suggested model. We assessed the endemic and disease free equilibrium, reproductive number, strength number, and parameter sensitivity, and examined the global stability of the proposed system. The existence, uniqueness, and Hilfer generalized proportional operators for the constant of proportionality of the system’s solutions are demonstrated using fixed-point theorems. We simulated a system of fractional differential equations analytically using the Laplace Adomian Decomposition Method (LADM). This study is important since it is the first to model mumps related hearing loss using a fractional order model based on hybrid fractional operators without a singular kernel. The fractional-order derivative retains the system memory effect, is nonlocal, and outperforms the integer-order derivative in this regard. This sort of study aids medical professionals in diagnosis, treatment planning, and decision-making for mumps induced hearing loss.

A caputo fractional-order model of tuberculosis incorporating enlightenment and therapy using the Laplace-Adomian decomposition method

ABSTRACT In this study, we used a deterministic model to investigate tuberculosis transmission dynamics while considering control measures. We analyzed four compartmental models representing susceptible, latent, infected, and recovered populations. To assess the potential spread of the disease, we calculated the basic reproduction number using the next-generation matrix after establishing a disease-free equilibrium. Additionally, we explored the endemic equilibrium, as well as local and global stabilities. To obtain numerical solutions, we employed the Laplace-Adomian decomposition method. For constructing the model, we utilized Maple 18 software and varied the order (0 < ψ < 1) to examine the impact of enlightenment and therapy. Graphical representations were used to analyze the effects of non-integer order Caputo derivative parameters on the susceptible, latent, infected, and recovered populations over time. Our detailed discussion highlights the crucial role of mathematical models based on Caputo fractional derivatives in effectively controlling and eradicating tuberculosis from society. These findings contribute valuable insights to inform strategies for combating the disease and promoting public health initiatives.