scholarly journals A local radial basis function collocation method to solve the variable-order time fractional diffusion equation in a two-dimensional irregular domain

2018 ◽  
Vol 34 (4) ◽  
pp. 1209-1223 ◽  
Author(s):  
Song Wei ◽  
Wen Chen ◽  
Yong Zhang ◽  
Hui Wei ◽  
Rhiannon M. Garrard
Keyword(s):  
Diffusion Equation ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Variable Order ◽  
Two Dimensional ◽  
Irregular Domain ◽  
Time Fractional Diffusion Equation

Wellposedness and regularity of a variable-order space-time fractional diffusion equation

2020 ◽  
Vol 18 (04) ◽  
pp. 615-638 ◽  
Author(s):  
Xiangcheng Zheng ◽  
Hong Wang
Keyword(s):  
Diffusion Equation ◽  
Linear Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Variable Order ◽  
Order Linear ◽  
Integer Order ◽  
Time Fractional Diffusion Equation ◽  
Full Regularity

We prove wellposedness of a variable-order linear space-time fractional diffusion equation in multiple space dimensions. In addition we prove that the regularity of its solutions depends on the behavior of the variable order (and its derivatives) at time [Formula: see text], in addition to the usual smoothness assumptions. More precisely, we prove that its solutions have full regularity like its integer-order analogue if the variable order has an integer limit at [Formula: see text] or have certain singularity at [Formula: see text] like its constant-order fractional analogue if the variable order has a non-integer value at time [Formula: see text].

scholarly journals An inverse source problem for a two dimensional time fractional diffusion equation with involution

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
B. J. Kadirkulov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Diffusion Equation ◽  
Fourier Method ◽  
Dirichlet Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation

In this paper, we consider a two-dimensional generalization of the parabolic equation. Using the Fourier method, we study the solvability of the inverse problem with the Dirichlet condition and periodic conditions.

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