Adomian Decomposition Method for Solving Delay Differential Equations of Fractional Order

Mohammed, Osama H.; Khlaif, Abbas I.

doi:10.9790/5728-10610105

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…They give approximations of the analytic solution of the DDEs explicitly. There exist several numerical schemes [1][2][3] developed and implemented over the years for solving DDEs. Many of these numerical methods are quite explicit and straightforward exhibiting a great sense of convergence.…”

Section: Introduction mentioning

confidence: 99%

Reconstructed Elzaki Transform Method for Delay Differential Equations with Mamadu-Njoseh Polynomials

Mamadu¹,

Ojarikre²

2019

JMSS

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One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transform method (ETM)) for computing delay differential equations (DDEs). Here, a reconstructed Elzaki transform method (RETM) is proposed for the solution of DDEs where Mamadu-Njoseh polynomials are applied as basis functions in the approximation of the analytic solution. Using this strategy, a numerical illustration as in Ref.[1] is provided to the RETM as a basis for comparison to guarantee accuracy and consistency of the method. All numerical computations were performed with MAPLE 18 software.

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Section: Introduction mentioning

confidence: 99%

Reconstructed Elzaki Transform Method for Delay Differential Equations with Mamadu-Njoseh Polynomials

Mamadu¹,

Ojarikre²

2019

JMSS

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“…Wang [29] combined the Adams-Bashforth-Moulton method with the linear interpolation method to find an approximate solution for FDDEs. Mohammed and Khlaif [17] applied the Adomian decomposition method to get the numerical solution of FDDEs. Mousa-Abadian and Momeni-Masuleh proposed a numerical scheme to solve linear fractional delay differential systems [19].…”

Section: Introductionmentioning

confidence: 99%

On mixed steps-collocation schemes for nonlinear fractional delay differential equations

Mousa-Abadian¹,

Momeni-Masuleh²

2019

Preprint

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This research deals with the numerical solution of non-linear fractional differential equations with delay using the method of steps and shifted Legendre (Chebyshev) collocation method. This article aims to present a new formula for the fractional derivatives (in the Caputo sense) of shifted Legendre polynomials. With the help of this tool and previous work of the authors, efficient numerical schemes for solving non-linear continuous fractional delay differential equations are proposed. The proposed schemes transform the nonlinear fractional delay differential equations to a non-delay one by employing the method of steps. Then, the approximate solution is expanded in terms of Legendre (Chebyshev) basis. Furthermore, the convergence analysis of the proposed schemes is provided. Several practical model examples are considered to illustrate the efficiency and accuracy of the proposed schemes.

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“…Fractional delay differential equations are a very recent topic and it is a generalization of the delay differential equations to arbitrary non-integer order. Most fractional delay differential equations have no exact solutions therefore different numerical methods such as [16][17][18][19][20][21] have been developed and applied for providing approximate solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Fractional delay differential equations have found many applications in control theory, [21], agriculture [22], Chaos [23][24][25][26][27], and bioengineering [ 28,29] and so on.…”

Section: Introductionmentioning

confidence: 99%

Computational Method based Laplace Adomian Decomposition for Solving Delay Differential Equations of Fractional Order

Mohammed

2018

JNUS

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In this paper we present a computational method for solving delay differential equations of fractional order by employing the Laplace Adomian decomposition method. This method is combined from the Laplace transforms and the Adomian decomposition method taking into account the Caputo derivative as a motivation to describe the fractional derivative. The method is a modification of the Adomian decomposition method and is tested on two examples in order to illustrate the pertinent feature of this method the results shows that the proposed method is an effective and powerful tool for solving delay differential equations of fractional order. A comparison with the exact solution and with the existing methods such as Adomian decomposition method and homotopy analysis method is made.

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Adomian Decomposition Method for Solving Delay Differential Equations of Fractional Order

Cited by 10 publications

References 17 publications

Reconstructed Elzaki Transform Method for Delay Differential Equations with Mamadu-Njoseh Polynomials

Reconstructed Elzaki Transform Method for Delay Differential Equations with Mamadu-Njoseh Polynomials

On mixed steps-collocation schemes for nonlinear fractional delay differential equations

Computational Method based Laplace Adomian Decomposition for Solving Delay Differential Equations of Fractional Order

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