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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Variational formulation of time-fractional parabolic equations
TL;DR: In this article, the authors considered the initial/boundary value problems for parabolic PDE ∂ t α u − Δ u = f with fractional Caputo derivative ∆ t α of order 1 ∕ 2 α 1 as time derivative and the usual Laplacian − Δ as space derivative, and proved wellposedness of corresponding variational formulations based entirely on fractional Sobolev-Bochner spaces.
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A Tikhonov regularization method for solving a backward time-space fractional diffusion problem
TL;DR: In this paper , a backward problem for a time-space fractional diffusion equation is considered, which is to determine the initial data from a noisy final data, and a Tikhonov regularization method is constructed.
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On a backward problem for inhomogeneous time-fractional diffusion equations
TL;DR: The main goal of this paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method.
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Filter regularization for final value fractional diffusion problem with deterministic and random noise
TL;DR: A regularized solution using the filter regularization method in both cases: the deterministic case and random noise case is constructed using both parameter choice rule methods and a-priori and the a-posteriori methods.
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Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel
TL;DR: In this paper , stable numerical schemes for generalized time-fractional diffusion equations (GTFDEs) with smooth and non-smooth solutions on the non-uniform grid were developed.
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.