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Existence and uniqueness of time-fractional diffusion equation on a metric star graph
TLDR
In this paper, the authors studied the time-fractional diffusion equation on a metric star graph and proved the existence and uniqueness of the weak solution based on eigenfunction expansions.Abstract:
In this paper, we study the time-fractional diffusion equation on a metric star graph. The existence and uniqueness of the weak solution are investigated and the proof is based on eigenfunction expansions. Some priori estimates and regularity results of the solution are proved.read more
Citations
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Source identification for the heat equation with memory
TL;DR: A stable efficient identification algorithm is proposed which reduces essentially to solving linear integral Volterra equations of the second kind for source identification problems for the heat equation with memory on an interval and on graphs without cycles.
Cauchy Problem for Subdiffusion Equation on Metric Star Graph with Edge Dependent Order of Time-Fractional Derivative
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An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data
Aiguo Xiao,Xueyang Li +1 more
TL;DR: In this paper , a space-time sparse grid (STSG) method was proposed to solve the d-dimensional time-fractional diffusion equation (TFDE) in order to improve the convergence rate.
References
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Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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Theory and Applications of Fractional Differential Equations
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.
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Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
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Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
TL;DR: 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.