Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations

Song, Junqiang; Yin, Fukang; Cao, Xiaoqun; Lu, Fengshun

doi:10.1155/2013/392567

Cited by 8 publications

(12 citation statements)

References 45 publications

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“…For example, J. Song et al in [11] have applied Fractional Variational Iteration Method (FVIM) for the solutions of some FPDEs. Duan et al have used Adoman's Decomposition Method (ADM) to obtain series form solutions of different Partial Differential Equations (PDEs) and FPDEs with initial and boundary conditions [12].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method

2019

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In this article, the ( G ′ / G ) -expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie’s operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in ( G ′ / G ) , where G = G ( ξ ) satisfies a second order linear ordinary differential equation. In this paper, ( G ′ / G ) -expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions.

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Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method

2019

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“…This technique is based on the modified Riemann-Liouville derivative. Recently, there are many interesting works that have been considered to solve various fractional differential equations (Elbeleze et al, 2013;Faraz et al, 2011;Song et al, 2013;Wu and Lee, 2010). A correction functional is constructed by the general Lagrange multiplier which can be found optimally through the variational theory.…”

Section: Introductionmentioning

confidence: 99%

An efficient computational technique for solving the Fokker–Planck equation with space and time fractional derivatives

Saravanan¹,

Magesh²

2016

Journal of King Saud University - Science

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This paper presents numerical solutions of the linear and nonlinear Fokker-Planck partial differential equations [FPPDEs] with space and time fractional derivatives through analytical solutions. These are treated by two analytical methods, namely, fractional reduced differential transform method [FRDTM] and fractional variational iteration method [FVIM] followed by some examples. Numerical results obtained by both FRDTM and FVIM are compared with some existing methods in the literature. This comparison shows the supremacy of FRDTM over FVIM and existing methods in terms of accuracy, simplicity and reliability. ª 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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“…Yin et al [13] also couple the VIM with Legendre wavelets for the solution of nonlinear PDEs. Song et al [14] compare the results obtained by the fractional VIM and ADM concluding that the methodologies are similar; however, the VIM does not require the calculation of Adomian polynomials. Atangana and Kılıçman [15] couple the Homotopy perturbation method (HPM) with the Sumudu transform, an integral transform similar to the Laplace transform, to obtain solutions to certain nonlinear heat-like FPDEs.…”

Section: Introductionmentioning

confidence: 99%

Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations

Jacobs

Harley

2014

Abstract and Applied Analysis

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A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.

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Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations

Cited by 8 publications

References 45 publications

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method

An efficient computational technique for solving the Fokker–Planck equation with space and time fractional derivatives

Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations

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