scholarly journals Initial value problem for the $$(2+1)$$-dimensional time-fractional generalized convection–reaction–diffusion wave equation: invariant subspaces and exact solutions

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
P. Prakash ◽  
K. S. Priyendhu ◽  
K. M. Anjitha
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Initial Value Problem ◽  
Invariant Subspaces ◽  
Reaction Diffusion ◽  
Initial Value ◽  
Diffusion Wave

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.

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