Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation

“…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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“…Keeping all this in mind, various type of vigorous techniques has been developed to find an approximate solution of such type of fractional differential equations, among others, generalized differential transform method [7], variational iteration method [8], local fractional variational iteration method [9], reproducing kernel Hilbert space method [10], Adomian decomposition method [11] and homotopy analysis method [12], Fractional reduced differential transform method [13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay

Singh

Kumar

2017

SeMA

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Abstract. This paper deals the implementation of homotopy perturbation transform method (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay, including generalized Burgers equations with proportional delay. The HPTM is a hybrid of Laplace transform and homotopy perturbation method. To confirm the efficiency and validity of the method, the computation of three test problems of TFPDEs with proportional delay presented. The proposed solutions are obtained in series form, converges very fast. The scheme seems very reliable, effective and efficient powerful technique for solving various type of physical models arising in sciences and engineering.

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Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation

Cited by 63 publications

References 41 publications

Numerical method for solving fractional coupled Burgers equations

Numerical method for solving fractional coupled Burgers equations

Numerical method for fractional dispersive partial differential equations

Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay

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