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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Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
TL;DR: Two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method are developed and establish error estimates optimal with respect to the regularity of problem data.
Journal ArticleDOI
The Galerkin finite element method for a multi-term time-fractional diffusion equation
TL;DR: The initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain is considered and nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived.
Journal ArticleDOI
An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
TL;DR: In this article, the error analysis of the L1 scheme was revisited, and an O( √ 2−ε ) convergence rate was established for both smooth and nonsmooth initial data.
Journal ArticleDOI
A tutorial on inverse problems for anomalous diffusion processes
Bangti Jin,William Rundell +1 more
TL;DR: In this article, the degree of ill-posedness of fractional diffusion inverse problems was examined using the two-parameter Mittag-Leffler function and singular value decomposition.
References
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Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.
Posted Content
Fractional Calculus: Integral and Differential Equations of Fractional Order
TL;DR: In this article, the authors introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus, and derive the analytical solutions of the most simple linear integral and differential equations in fractional order.
Book
Evolutionary integral equations and applications
TL;DR: In this article, the authors deal with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space, where the main feature of the kernels involved is that they consist of unbounded linear operators.
Posted Content
Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
TL;DR: In this article, the authors review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics.
Journal ArticleDOI
Fractional diffusion and wave equations
W. R. Schneider,W. Wyss +1 more
TL;DR: In this article, the Green's function of fractional diffusion is shown to be a probability density and the corresponding Green's functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited.