Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation

2019 ◽  
Vol 83 (4) ◽  
pp. 1509-1530 ◽  
Author(s):  
Fan Yang ◽  
Yan Zhang ◽  
Xiao-Xiao Li
Keyword(s):  
Wave Equation ◽  
Iterative Method ◽  
Initial Value Problem ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
Time Space

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

Solution of fractional partial differential equations using iterative method

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Chandradeepa Dhaigude ◽  
Vasant Nikam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
Fractional Partial Differential Equations ◽  
Initial Value ◽  
Diffusion Wave ◽  
Linear And Nonlinear

AbstractThe purpose of this paper is to obtain solutions for both linear and nonlinear initial value problems (IVPs) for fractional transport equations and fractional diffusion-wave equations using the iterative method.

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