Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation

Rajeev, .; Kushwaha, Mohan Singh

doi:10.1016/j.apm.2012.07.047

Cited by 32 publications

(9 citation statements)

References 30 publications

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“…Martin et al [23] also discussed the physical basis for anomalous diffusion in bed load transport. Rajeev and Kushwaha [24] also discussed a mathematical model with time-fractional derivative for a moving boundary problem which occurs in sedimentation process. These models motivate to discuss space-time fractional diffusion model in sedimentation process to study the physical effect in complex domain.…”

Section: Introductionmentioning

confidence: 97%

An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

Rajeev

Kushwaha

Kumar

2013

Ain Shams Engineering Journal

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A mathematical model of the movement of the shoreline in a sedimentary ocean basin is discussed. The model includes space-time fractional derivative in Caputo sense and variable latent heat term. An approximate solution of the problem is obtained by Adomian decomposition method and the results thus obtained are compared graphically with an exact solution of integer order (b = 1, a = 1). Three particular cases, the standard diffusion, the time-fractional and the spacefractional diffusions are also discussed. The model and solution are generalization of previous works.

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Section: Introductionmentioning

confidence: 97%

An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

Rajeev

Kushwaha

Kumar

2013

Ain Shams Engineering Journal

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“…Many analytical algorithms have been investigated analytically to obtain closed form solutions in treating FDEs such as variational iteration method, Fourier transform method, the homotopy analysis method, the method of separation of variables, Adomian decomposition method, and Laplace transform method [10,23,[27][28][29]. However, there are only a few types of these equations in which the analytical solutions are available.…”

Section: Introductionmentioning

confidence: 99%

An efficient fractional polynomial method for space fractional diffusion equations

Krishnaveni

Kannan

Balachandar

et al. 2018

Ain Shams Engineering Journal

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In this paper, we develop a new approximation technique for solving space fractional diffusion equation. The method of solution is based on fractional order Legendre function with the concept of Caputo's definition of fractional derivatives. Convergence analysis and error bound of the method are discussed. Several Illustrative examples are included to demonstrate the validity and applicability of the proposed method. The obtained results reveal that the method is more accurate and efficient than the methods such as Chebyshev finite difference method and Tau approach method discussed in the literature. Ó 2016 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. 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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“…Another examples of application of the variational iteration method can be found in papers [17,18] as well as in references included in these works. Next, in paper [20] there is presented the Stefan problem governed by fractional diffusion equation. Next, in paper [20] there is presented the Stefan problem governed by fractional diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

A certain analytical method used for solving the Stefan problem

et al. 2013

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The paper presents an analytic method applied for finding the approximate solution of Stefan problem reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial extension of a sought function describing the field of temperature into the power series, some coefficients of which can be determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which can be obtained by solving the appropriate differential equations. Results received by applying the proposed procedure will be compared with the results obtained with the aid of a classical numerical method served for solving the Stefan problem

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Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation

Cited by 32 publications

References 30 publications

An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

An efficient fractional polynomial method for space fractional diffusion equations

A certain analytical method used for solving the Stefan problem

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