scholarly journals Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation

2022 ◽  
Vol 507 (1) ◽  
pp. 125741
Author(s):  
Luciano Abadias ◽  
Edgardo Alvarez ◽  
Stiven Díaz
Keyword(s):  
Diffusion Equation ◽  
Large Time ◽  
Fractional Diffusion ◽  
Large Time Behavior ◽  
Fractional Diffusion Equation ◽  
Time Behavior ◽  
Time Fractional Diffusion Equation

scholarly journals Cauchy problem for general time fractional diffusion equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1545-1559
Author(s):  
Chung-Sik Sin
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Source Term ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Time Behavior ◽  
Analysis Technique ◽  
The Cauchy Problem ◽  
Long Time ◽  
Time Fractional Diffusion Equation

Abstract In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis technique. Then, based on the representation of the solution of the inhomogenous linear ordinary differential equation with the general Caputo-type operator, the general diffusion equation with source term is studied.

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