Variational iteration method for the time-fractional Fornberg–Whitham equation

Sakar, Mehmet Giyas; Erdoğan, Fevzi; Yıldırım, Ahmet

doi:10.1016/j.camwa.2012.01.031

Cited by 62 publications

(43 citation statements)

References 34 publications

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“…Odibat et.al [39] and Molliq et al [40] applied VIM to solve fractional Zakharov-Kuznetsov equations. J. Lu [41] and Sakar et al [42][43] applied VIM and AVIM to Fornberg-Whitham equation and by others for different models [44][45][46][47]. The proposed FVIM do not need perturbation, discretization or linearization unlike the technique argued in the literature.…”

Section: Introductionmentioning

confidence: 99%

Numerical method for fractional dispersive partial differential equations

Prakash¹,

Kumar²

2017

Communications in Numerical Analysis

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In this work, fractional variational iteration method (FVIM) has been applied successfully to find the solution of fractional dispersive partial differential equations of third-order in multi-dimensional spaces. The contemplated graphs explain the character of the solution for different values of fractional order . The mightiness and accurateness of the proposed techniques are studied with the help of two test examples.

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Section: Introductionmentioning

confidence: 99%

Numerical method for fractional dispersive partial differential equations

Prakash¹,

Kumar²

2017

Communications in Numerical Analysis

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“…Various definitions and basic concept of fractional calculus are present in many books [1][2][3][4]. Therefore, several analytical and numerical methods were developed for solutions of fractional differential equations (both linear and nonlinear), among which Adomian's decomposition method [5][6][7], variation iteration method [8,9], homotopy perturbation method [10][11][12], homotopy analysis method [13][14][15], homotopy asymptotic method [16][17][18],differential transform method [19], and Galerkin method [20].…”

Section: Introductionmentioning

confidence: 99%

A Modified Analytical Approach for Fractional Discrete KdV Equations Arising in Particle Vibrations

Kumar

2017

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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In this paper, we present an effectiveness of the proposed analytical algorithm for nonlinear time fractional discrete KdV equations. The discrete KdV equation play an important role in modeling of complicated physical phenomena such as particle vibrations in lattices, current flow in electrical flow and pulse in biological chains. The proposed algorithm is amagalation of the homotopy analysis method, Laplace transform method and homotopy polynomials. First, we present an alternative framework of the proposed method which can be used simply and effectively to handle nonlinear problems arising in science and engineering. Then, mainly, we address the convergence study of nonlinear fractional differential equations with Laplace transform. Camparisons are made between the results of the proposed method and exact solutions. Illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method. The new results reveal that the proposed method is explicit, efficient and easy to use.

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“…Lu [9] applied a variational iteration method to obtain approximate solution of the Fornberg-Whitham equation. Sakar et al [10] and Prakash et al [11] have made use of the variational iteration method to find numerical solutions of time-fractional Fornberg-Whitham equation and fractional coupled Burger's equation respectively. Shakeri et al [12] solved the two dimensional biological population model for the standard case when α = 1 by a variational iteration method.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of two dimensional time fractional-order biological population model

Prakash

Kumar

2016

Open Physics

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Abstract:In this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional order α.

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Variational iteration method for the time-fractional Fornberg–Whitham equation

Cited by 62 publications

References 34 publications

Numerical method for fractional dispersive partial differential equations

Numerical method for fractional dispersive partial differential equations

A Modified Analytical Approach for Fractional Discrete KdV Equations Arising in Particle Vibrations

Numerical solution of two dimensional time fractional-order biological population model

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