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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An inverse problem for homogeneous time-fractional diffusion problem on the sphere
TL;DR: In this paper, the authors considered an inverse problem for the time-fractional diffusion equation on the sphere where the final data of the sphere are given, and the regularization method has to be used for the stable approximate solution.
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Optimal Control of a Fractional Diffusion Equation with Delay
Gisèle Mophou,Jean-Marie Fotsing +1 more
TL;DR: In this paper, a homogeneous Dirichlet boundary fractional diffusion equation with delay is studied and the optimal control problem associated to the controlled equivalent fractional fractional time derivative has a unique solution.
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On an inverse problem of nonlinear imaging with fractional damping.
TL;DR: In this article, the attenuated Westervelt equation in pressure formulation is considered and the attenuation is characterised by the inclusion of non-local operators that give power law damping as opposed to the exponential of classical models.
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On a time fractional diffusion with nonlocal in time conditions
TL;DR: In this article, the authors considered a fractional diffusion equation with nonlocal integral condition and gave a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions.
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L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term
TL;DR: In this paper , the authors proposed a method for solving time fractional diffusion equation with nonlocal diffusion term, which comprises L1 scheme on graded mesh, finite element method and Newton's method.
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.