BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER

By Yury F. Luchko. 2009

204 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84cacdc41b585f374e02f950849d53b6786169c0

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Citations in the corpus

Distributed-order fractional diffusions on bounded domains (2009, background): “Luchko [21] proved the uniqueness and continuous dependence on initial conditions on bounded domains.”
A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed‐order fractional damped diffusion‐wave equation (2018, background): “Substituting relations (52) to (57) in Equation 51 yields Nq ∑”
Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method (2017, background): “Such results are still very scarce and may be resumed in the following theorems (adapted from [44]).”
Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation (2014, background): “Luchko [2,3] and the references therein), which is given by:”
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications (2014, unknown): “Extended maximum principles for the multi-term time-fractional diffusion equation and for the time-fractional diffusion equation of the distributed order were introduced and applied in [11] and [9], respectively.”
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations (2014, methodology): “In [11], a first attempt to analyze the initial-boundaryvalue problems for the generalized distributed order time-fractional diffusion equation over an open bounded multi-dimensional domain has been undertaken.”
Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications (2016, background): “For more details on this topics the reader is welcome to consult [6, 13, 14, 15, 16, 17, 18] and the references therein.”
General Fractional Calculus, Evolution Equations, and Renewal Processes (2011, background): “where ρ is a Borel measure on [0, 1]; see [1, 6, 11, 14, 15, 16, 17, 21, 28].”
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013, background): “In [19], boundary value problems for the generalized time-fractional diffusion equation of distributed order over an open bounded domain G× [0, T ], G ∈ IRn were considered.”
Time fractional equations and probabilistic representation (2017, background): “8); see [10, 11, 15] for cases of ∂ t u = Lu and [13] for distributed order time fractional equation ∂w t u = Lu where L is a one-dimensional differential operator in a bounded interval.”