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 New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Diferential Equations
TL;DR: In this article, the singularity of the new basis function can be tailored to that of the singular solutions to a class of time-fractional PDEs, leading to spectrally accurate approximation.
Journal ArticleDOI
Identification of a source in a fractional wave equation from a boundary measurement
Katarina Šišková,Marián Slodička +1 more
TL;DR: Using the Rothe method the existence of the solution and the source term obeying the variational formulation and the equation obtained from applying the measurement on the equation is proven.
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A fractional space-time optimal control problem: analysis and discretization\
TL;DR: In this paper, a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative was studied and a fully-discrete scheme for the control and, for the state, first-degree tensor product finite elements in space and a finite difference discretization in time.
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On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative
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Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium.
Bangti Jin,Yavar Kian +1 more
TL;DR: In this paper, the authors investigated the recovery of a parameter in a diffusion process given by the order of derivation in time for some class of diffusion equations, including both classical and time-fractional diffusion equations.
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.