2013
DOI: 10.1137/130910865
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The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation

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Cited by 289 publications
(158 citation statements)
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“…There are two predominant approaches for approximating the fractional derivative: one approach is by using Lubich's convolution quadrature [27]- [29] and another approach is by using the L1 scheme (or Diethelm's finite difference method). For the recent developments for solving fractional ordinary (or partial ) differential equations by using the Lubich's convolution quadrature method, readers may refer to e.g., [39], [11], [3], [42], [6], [44], [46], [47], [22], [21], [19], etc.…”
mentioning
confidence: 99%
“…There are two predominant approaches for approximating the fractional derivative: one approach is by using Lubich's convolution quadrature [27]- [29] and another approach is by using the L1 scheme (or Diethelm's finite difference method). For the recent developments for solving fractional ordinary (or partial ) differential equations by using the Lubich's convolution quadrature method, readers may refer to e.g., [39], [11], [3], [42], [6], [44], [46], [47], [22], [21], [19], etc.…”
mentioning
confidence: 99%
“…Recent advances in the fractional calculus concern the fractional derivative modeling in applied science, see [2,9,38], the theory of fractional differential equations, see [21], numerical approaches for the fractional differential equations, see [26,55] and the references therein. Another hot issue is the theory of hemivariational inequalities which is based on properties of the Clarke generalized gradient, defined for locally Lipschitz functions.…”
Section: Introductionmentioning
confidence: 99%
“…The corresponding fractional Fick's law has been proposed [4]. Recently, a modified fractional Fick's law has been used to describe processes that become less anomalous as time progresses by the inclusion of a secondary fractional time derivative acting on a diffusion operator [5], Till now, various kinds of anomalous diffusion equations have been studied numerically, see [7,8,9,10,11,12,13,14,15,16,17] and many the references cited therein. However, it seems that only a few numerical studies are available for the two-term subdiffusions of the above form.…”
Section: Introductionmentioning
confidence: 99%