Laplace decomposition for solving nonlinear system of fractional order partial differential equations

Khan, Hassan; Shah, Rasool; Băleanu, Dumitru; Arif, Muhammad

doi:10.1186/s13662-020-02839-y

Cited by 47 publications

(22 citation statements)

References 33 publications

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“…The Laplace Adomian Decomposition method [26] [27] [28] is used to find the solution to the fractional order SIR model. This method is simple to use, and the resulting series is convergent easily compared with other methods.…”

Section: Mathematical Modelling and Solution Of The Fractional Order Sir Modelmentioning

confidence: 99%

Numerical Analysis and Transformative Predictions of Fractional Order Epidemic Model during COVID-19 Pandemic: A Critical Study from Bangladesh

Chandrow¹,

Das²,

Shil³

et al. 2021

JAMP

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The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (R 0 ) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.

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Section: Mathematical Modelling and Solution Of The Fractional Order Sir Modelmentioning

confidence: 99%

Numerical Analysis and Transformative Predictions of Fractional Order Epidemic Model during COVID-19 Pandemic: A Critical Study from Bangladesh

Chandrow¹,

Das²,

Shil³

et al. 2021

JAMP

View full text Add to dashboard Cite

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“…Around the years, a great deal of study has been conducted in the fields of science and engineering all over the world, and various methodologies have been developed to provide the best obtainable solutions. is is an unstoppable process, and new techniques are being developed on a daily basis since the world is confronted with new, insoluble, and challenging difficulties and problems [18][19][20][21][22]. Different methods for solving FDEs have been proposed in the literature, including the fractional differential transform method (FDTM) [23], modified homotopy perturbation method (MHPM) [24], Adomian decomposition method (ADM) [25], Sumudu transform method (STM) [26], differential transform method (DTM) [27], homotopy analysis method (HAM) [28], variational iteration method (VIM) [29], and fractional Fourier transform method (FFTM) [30].…”

Section: Introductionmentioning

confidence: 99%

Analytical Investigation of Noyes–Field Model for Time‐Fractional Belousov–Zhabotinsky Reaction

et al. 2021

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In this article, we find the solution of time-fractional Belousov–Zhabotinskii reaction by implementing two well-known analytical techniques. The proposed methods are the modified form of the Adomian decomposition method and homotopy perturbation method with Yang transform. In Caputo manner, the fractional derivative is used. The solution we obtained is in the form of series which helps in investigating the analytical solution of the time-fractional Belousov–Zhabotinskii (B-Z) system. To verify the accuracy of the proposed methods, an illustrative example is taken, and through graphs, the solution is shown. Also, the fractional-order and integer-order solutions are compared with the help of graphs which are easy to understand. It has been verified that the solution obtained by using the given approaches has the desired rate of convergence to the exact solution. The proposed technique’s principal benefit is the low amount of calculations required. It can also be used to solve fractional-order physical problems in a variety of domains.

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“…Several of the main tools used in solving this type of equations are LADM, VIM, and homotopy. It should be noted that LADM effects have shown higher accuracy as compared to other methods in the literature [7]. LADM and the VIM are comparatively new approaches to fit an analytical approximation to linear and nonlinear problems [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations

Mohamed

Elzaki

Algolam

et al. 2021

Journal of Applied Mathematics

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The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series which are facilely computable.

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Laplace decomposition for solving nonlinear system of fractional order partial differential equations

Cited by 47 publications

References 33 publications

Numerical Analysis and Transformative Predictions of Fractional Order Epidemic Model during COVID-19 Pandemic: A Critical Study from Bangladesh

Numerical Analysis and Transformative Predictions of Fractional Order Epidemic Model during COVID-19 Pandemic: A Critical Study from Bangladesh

Analytical Investigation of Noyes–Field Model for Time‐Fractional Belousov–Zhabotinsky Reaction

New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations

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