Numerical solutions of the initial value problem for fractional differential equations by modification of the Adomian decomposition method

AbstractIn this paper, we extend a reliable modification of the Adomian decomposition method presented in [34] for solving initial value problem for fractional differential equations.In order to confirm the applicability and the advantages of our approach, we consider some illustrative examples.

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One Solution of Multi-term Fractional Differential Equations by Adomian Decomposition Method: Scientific Explanation

Current Topics on Mathematics and Computer Science Vol. 6 ◽

10.9734/bpi/ctmcs/v6/11542d ◽

2021 ◽

pp. 120-130

Author(s):

Abdollah Sadeghinia ◽

Prabhat Kumar

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Decomposition Method ◽

Scientific Explanation ◽

Adomian Decomposition Method ◽

Adomian Decomposition ◽

Fractional Differential

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Solving a system of nonlinear fractional differential equations using mahgoub adomian decomposition method

Bulletin of Pure & Applied Sciences- Mathematics and Statistics ◽

10.5958/2320-3226.2019.00043.2 ◽

2019 ◽

Vol 38e (1) ◽

pp. 396

Author(s):

S. Katrin Lydia

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Nonlinear Fractional Differential Equations ◽

Adomian Decomposition ◽

Fractional Differential

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The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2013.01.019 ◽

2013 ◽

Vol 66 (5) ◽

pp. 728-736 ◽

Cited By ~ 29

Author(s):

Jun-Sheng Duan ◽

Temuer Chaolu ◽

Randolph Rach ◽

Lei Lu

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Convergence Acceleration ◽

Nonlinear Fractional Differential Equations ◽

Acceleration Techniques ◽

Adomian Decomposition ◽

Fractional Differential

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

Journal of Applied Mathematics ◽

10.1155/2021/6662645 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Mohamed Z. Mohamed ◽

Tarig M. Elzaki ◽

Mohamed S. Algolam ◽

Eltaib M. Abd Elmohmoud ◽

Amjad E. Hamza

Keyword(s):

Differential Equations ◽

Decomposition Method ◽

Numerical Solutions ◽

Adomian Decomposition Method ◽

Variational Iteration Method ◽

Transform Method ◽

Variational Iteration ◽

Modified Method ◽

Adomian Decomposition ◽

Fractional Differential

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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