Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
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In this paper, the authors considered the initial value/boundary value problems for fractional diffusion-wave equation and established the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2011-10-01 and is currently open access. It has received 965 citations till now. The article focuses on the topics: Boundary value problem & Initial value problem.read more
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A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity
Haiyu Liu,Shujuan Lü +1 more
TL;DR: In this article, a high-order numerical scheme for nonlinear time fractional reaction-diffusion equations with initial singularity was proposed, where L2-1 σ scheme on graded mesh is used to approximate Caputo fractional derivative and Legendre spectral method is applied to discrete spatial variable.
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Error estimates of a discontinuous Galerkin method for time fractional diffusion problems with nonsmooth data
Binjie Li,Hao Luo,Xiaoping Xie +2 more
TL;DR: In this paper, a discontinuous Galerkin method for time fractional diffusion problems is proposed, which uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in spatial discretisation.
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Identification of an inverse source problem for time‐fractional diffusion equation with random noise
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An Exponentially Convergent Scheme in Time for Time Fractional Diffusion Equations with Non-smooth Initial Data
Beiping Duan,Zhoushun Zheng +1 more
TL;DR: The algorithm is motivated by the discovery that the solution in temporal direction possesses high regularity in proper weighted Sobolev space on a special mesh in piecewise sense, and is extended to solve time-fractional diffusion equations with initial data.
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On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion
TL;DR: In this paper , two final value problems for fractional reaction equation with standard Brownian motion W ( t ) and fractional Brownian motions B H ( t ), for H ∈ ( 1 4 , 1 2 ) ∪ ( 1 2 , 1 ) were investigated under strongly choices of data.
References
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TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.