scholarly journals Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations

2022 ◽  
Vol 6 (1) ◽  
pp. 32
Author(s):  
Hegagi Mohamed Ali ◽  
Hijaz Ahmad ◽  
Sameh Askar ◽  
Ismail Gad Ameen
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Fractional Pdes ◽  
Adomian Decomposition ◽  
Vorticity Transport ◽  
The Given

In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity transport, dispersal in porous media, and hydrodynamic turbulence. The analysis of these methods is implemented on the BK, Burgers systems and solutions have been offered in a simple formula. We show our results in figures and tables to demonstrate the efficiency and reliability of the used methods. Furthermore, our outcome converges rapidly to the given exact solutions.

scholarly journals Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 335 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Poom Kumam
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
In Series

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

scholarly journals On some nonlinear fractional PDEs in physics

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 59-69
Author(s):  
Jamshad Ahmad ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Inverse Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Pdes ◽  
The Given ◽  
Nonlinear Nature

In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find approximate solution of time- fractional Fornberg-Whitham and time-fractional Wu-Zhang equations. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs arising in mathematical physics and hence can be extended to other problems of diversified nonlinear nature. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the proposed algorithm.  DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11687BIBECHANA 12 (2015) 59-69 

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

2021 ◽  
Vol 20 ◽  
pp. 712-716
Author(s):  
Zainab Mohammed Alwan
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method

2014 ◽  
Vol 6 (01) ◽  
pp. 107-119 ◽  
Author(s):  
D. B. Dhaigude ◽  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Discrete Schrödinger Equation ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation. The obtained solution is verified by comparison with exact solution whenα= 1.

scholarly journals Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

Solution methodology of convection boundary layer problems using Adomian decomposition method

2012 ◽  
Vol 227 (7) ◽  
pp. 1554-1565
Author(s):  
MJ Javanmardi ◽  
K Jafarpur ◽  
M Mahzoon
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Convection Boundary Layer ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Convection Boundary ◽  
Boundary Layer Problems

Adomian decomposition method has been applied to some convection boundary layer problems. It is shown that the method is excellent in solving nonlinear partial differential equations. Comparison of the results so obtained and those from conventional methods proves the technique to be powerful and to give nearly exact solutions. Since most physical problems are governed by nonlinear ordinary or partial differential equations, application of this method may be advised to simplify the method of solution.

scholarly journals Solving Some Derivative Equations Fractional Order Nonlinear Partials Using the Some Blaise Abbo Method

2021 ◽  
Vol 13 (2) ◽  
pp. 101
Author(s):  
Abdoul wassiha NEBIE ◽  
Frederic BERE ◽  
Bakari ABBO ◽  
Youssouf PARE
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Adomian Decomposition ◽  
Diffusion Convection

In this paper, we propose the solution of some nonlinear partial differential equations of  fractional order that modeled diffusion, convection and reaction problems. For the solution of these equations we will use the SBA method which is a method based on the combination of the Adomian Decomposition Method (ADM), the Picard's principle  and the method of successive approximations.   

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