Generalized differential transform method: Application to differential equations of fractional order

Odibat, Zaid; Momani, Shaher; Ertürk, Vedat Suat

doi:10.1016/j.amc.2007.07.068

Cited by 178 publications

(126 citation statements)

References 11 publications

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“…This MSDTM offers accurate solutions over a longer time frame (more stable) compared to the standard DTM. Using the theorems given in [12] and taking the differential transform for the system (8) with respect to time t gives…”

Section: Msdtm Algorithmmentioning

confidence: 99%

“…Also, they are closely related to fractals which are abundant in biological systems. It has been shown that the approximated solutions obtained using DTM are not valid for large t for some systems [12,13,14,15]. Therefore, we use the MSDTM to solve the following fractional order model of HTLV-I infection of CD4 + T-Cells of order 0 < α ≤ 1 :…”

Section: Msdtm Algorithmmentioning

confidence: 99%

“…Our motivation for this work is to obtain the approximate solution of the fractional modle of HTLV-I infection of CD4 + T-Cells using the multi-step differential transform method (MSDTM). This method is only a simple modification of the differential transform method (DTM) [12,13,14,15], in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of the multi-step diﬀerential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Zurigat

Ababneh

2015

JMA

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Section: Msdtm Algorithmmentioning

confidence: 99%

Section: Msdtm Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of the multi-step diﬀerential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Zurigat

Ababneh

2015

JMA

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“…Another important advantage is that this method is capable of greatly reducing the size of computational work while still accurately providing the series solution with fast convergence rate. The DTM have been studied widely in physics and mathematics [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method

2015

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Abstract:In this work, we present a dynamic behavior of the avian-human in uenza epidemic model by using ecient computational algorithm, namely the multistage differential transform method(MsDTM). The MsDTM is used here as an algorithm for approximating the solutions of the avian-human in uenza epidemic model in a sequence of time intervals. In order to show the e ciency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method (RK4M) and di erential transform method(DTM) solutions. It is shown that the MsDTM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RK4M.

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“…This method was introduced by Zhou (1986) to solve initial value problems in analysis of the electrical circuits. After that, DTM applied to differential algebraic equation Liu and Song, 2007) partial differential equation (Ayaz, 2003Ravi-Kanth and Aruna, 2008;Yang et al, 2006;Chang and Chang, 2009), integral equation (Odibat, 2008;Ozkol, 2005, 2008), ordinary differential equation (Mosayebidorcheh, 2014;Mosayebidorcheh and Mosayebidorcheh, 2012;Torabi and Aziz, 2012;Joneidi et al, 2009) and fractional differential equation (Nazari and Shahmorad, 2010;Odibat et al, 2008;Erturk et al, 2008;Arikoglu and Ozkol, 2007). The method is an iterative technique to find the Taylor series solution of the problem.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

Mosayebidorcheh¹,

Mosayebidorcheh²,

Rashidi³

2014

Sci. Res. Essays

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In this paper, a similarity transformation is used to reduce the three-dimensional steady state condensation film on an inclined rotating disk by a set of nonlinear boundary value problems. This problem is solved using a new hybrid technique based on differential transform method (DTM) and Iterative Newton's Method (INM). The differential equations and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated. After finding Jacobian matrix, the unknown parameters computed using Multi-Variable Iterative Newton's Method. These techniques are used to obtain an approximate solution of the problem. In this solution, there is no need to restrictive assumptions or linearization. The results compared with the numerical solution of the problem, and a good accuracy of the proposed hybrid method observed. Finally, the velocity and temperature profiles demonstrated for different values of problem parameters.

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Generalized differential transform method: Application to differential equations of fractional order

Cited by 178 publications

References 11 publications

Application of the multi-step diﬀerential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Application of the multi-step diﬀerential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

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