Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition

2009 ◽  
Vol 208 (2) ◽  
pp. 434-439 ◽  
Author(s):  
Xicheng Li ◽  
Mingyu Xu ◽  
Xiaoyun Jiang
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Moving Boundary ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Homotopy Perturbation ◽  
Moving Boundary Condition ◽  
Time Fractional Diffusion Equation

Analytical Approximate Solution of Space-Time Fractional Diffusion Equation with a Moving Boundary Condition

2011 ◽  
Vol 66 (5) ◽  
pp. 281-288 ◽  
Author(s):  
Subir Das ◽  
Rajnesh Kumar ◽  
Praveen Kumar Gupta
Keyword(s):  
Diffusion Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Approximate Analytic Solution ◽  
Approximate Analytical Solutions ◽  
Moving Boundary Condition ◽  
Time Fractional Diffusion Equation

August 12, 2010 The homotopy perturbation method is used to find an approximate analytic solution of the problem involving a space-time fractional diffusion equation with a moving boundary. This mathematical technique is used to solve the problem which performs extremely well in terms of efficiency and simplicity. Numerical solutions of the problem reveal that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

2010 ◽  
Vol 65 (10) ◽  
pp. 793-799 ◽  
Author(s):  
Subir Das ◽  
Subir Rajeev
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Iteration Method ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Diffusion ◽  
Adomian Decomposition ◽  
Moving Boundary Condition

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

scholarly journals Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
L. L. Sun ◽  
X. B. Yan
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Source Function ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Time Fractional Diffusion Equation ◽  
Continuation Technique

This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data. The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method. We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation. Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle. The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.

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