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A generalized differential transform method for linear partial differential equations of fractional order
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Elsevier B.V.
, 2007 , Article)
In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with space- and time-fractional ...
The modified homotopy perturbation method for solving strongly nonlinear oscillators
(
Elsevier
, 2009 , Article)
In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé approximants. This modified homotopy ...
Numerical comparison of methods for solving a special fourth-order boundary value problem
(
Elsevier Inc.
, 2007 , Article)
In this paper, we implement relatively new analytical techniques, the differential transform method, Adomian decomposition, and homotopy perturbation method, for solving a fourth-order boundary value problem. In these ...
Homotopy perturbation method for nonlinear partial differential equations of fractional order
(
Elsevier B.V.
, 2007 , Article)
The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is ...
Numerical methods for nonlinear partial differential equations of fractional order
(
Elsevier B.V.
, 2008 , Article)
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The ...
Application of generalized differential transform method to multi-order fractional differential equations
(
Elsevier
, 2007 , Article)
In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a ...
Solving fractional diffusion and wave equations by modified homotopy perturbation method
(
Elsevier B.V.
, 2007 , Article)
This Letter applies the modified He's homotopy perturbation method (HPM) suggested by Momani and Odibat to obtaining solutions of linear and nonlinear fractional diffusion and wave equations. The fractional derivative is ...
Solving systems of fractional differential equations using differential transform method
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Elsevier B.V.
, 2007 , Article)
This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application ...
Application of Homotopy Perturbation Method to Singularly Perturbed Volterra Integral Equations
(
Asian Network for Scientific Information
, 2008 , Article)
In this study, the Homotopy-Perturbation Method (HPM) proposed by J.-H. He is adopted for solving singularly perturbed Volterra integral equations (SVIEs). Three numerical examples are given to demonstrate the effectiveness ...