A Modified Method for Solving Delay Differential Equations of Fractional Order

Mohammed, Osama H.; Wadi, Qutaiba

doi:10.9790/5728-1205040107

Cited by 6 publications

(5 citation statements)

References 7 publications

(6 reference statements)

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“…By comparing the both sides of equation 17, we get ( (19) Applying the invers Laplace transform on both sides of equations (18) and (19), therefore the recursive solutions are given below as:…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

“…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%

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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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Section: Adomian Decomposition Methodsmentioning

confidence: 99%

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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“…Delay differential equations (DDEs) can be defined in terms of derivative of the unknown function at a certain time, which is for values of times given previously (Smith, 2011). Similar definitions are found in Avci (2022); Hameed and Wadi (2016). DDEs' contributions in the field of sciences and engineering are very significant (Smith, 2011).…”

Section: Introductionmentioning

confidence: 99%

Sufficient Conditions for Nonoscillation of Delay Differential Equations with Positive and Negative Coefficients using Schauder’s Fixed Point Theorem

Tahir,

Habib

2023

Nig J Bas App Sci

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Schauder’s fixed point theorem and its applications to delay differential equations (DDEs) cannot be over emphasized. In this work, interesting results regarding the sufficient conditions for nonoscillation of more generalized forms of DDEs are established and provides improvements on the results obtained in the past. However, applying the theorem and the characteristic equation of DDE with constant coefficients helps to determine those conditions. Lastly, to ascertain a claim from an existing literature for a solution that is on oscillatory and has such larger solutions, comparison theorem is used and the results are found to be true.

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“…Numerous techniques have been developed for the solutions of fractional differential equations (FDEs). These include, but not limited to, Adomian decomposition method (ADM), homotopy analysis method (HAM), homotopy perturbation method (HPM), Laplace transformation, variational iteration with Pade approximation, corrected Fourier series, natural decomposition method [25] , [26] , [27] , and fractional complex transformation [28] . The optimal q-HAM has also been used to solve fractional differential equations [29] .…”

Section: Introductionmentioning

confidence: 99%

A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus

2022

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A Modified Method for Solving Delay Differential Equations of Fractional Order

Cited by 6 publications

References 7 publications

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

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

Sufficient Conditions for Nonoscillation of Delay Differential Equations with Positive and Negative Coefficients using Schauder’s Fixed Point Theorem

A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus

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