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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Asymptotic behavior of solutions to space-time fractional diffusion equations
TL;DR: In this paper, the decay rate of the solution as t! 1 is dominated by the order of the time-fractional derivative of the diffusion derivative, which is the Laplace transform.
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Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation
TL;DR: In this paper, the uniqueness of a solution for an inverse source problem arising in linear time-fractional diffusion equations with time-dependent coefficients was studied and a new uniqueness result was formulated in Theorem 3.1.
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On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction-diffusion equation with delay
TL;DR: In this paper , the existence and uniqueness of a weak solution to a damped variable order fractional subdiffusion equation with time delay was proved under weak assumptions on the data, and the existence of the weak solution was established by the aid of derived a priori estimates.
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Mittag-Leffler Stabilization of an Unstable Time Fractional Hyperbolic PDE
TL;DR: This paper proposes an observer-based stabilizing control law, under which the closed-loop system is shown to admit a unique solution and to be Mittag–Leffler stable.
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A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions
TL;DR: A preconditioned fast divided-and-conquer finite element approximation for the initial-boundary value problem of variable-order time-fractional diffusion equations that derives a fast approximation of the coefficient matrix by the means of a sum of Toeplitz matrices multiplied by diagonal matrices.
References
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David Gilbarg,Neil S. Trudinger +1 more
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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.