scholarly journals Fourth-order numerical method for the space–time tempered fractional diffusion-wave equation

2017 ◽  
Vol 73 ◽  
pp. 120-127 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh ◽  
Weihua Deng
Keyword(s):  
Wave Equation ◽  
Numerical Method ◽  
Fourth Order ◽  
Fractional Diffusion ◽  
Space Time ◽  
Diffusion Wave

scholarly journals Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kangqun Zhang
Keyword(s):  
Wave Equation ◽  
Sobolev Space ◽  
Fractional Derivatives ◽  
Weighted Sobolev Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Existence Of Solution ◽  
Multiplier Theorem ◽  
Diffusion Wave ◽  
Loss Of Regularity

In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.

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