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• W4285288146 abstract "In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First, the asymptotic behavior of the fundamental solution of the fractional diffusion equation is considered. Then, we use the fundamental solution to obtain the representation formula of solutions of the Cauchy problem. In the last, the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math>-decay estimates for solutions are proved by employing the Fourier analysis technique." @default.
• W4285288146 created "2022-07-14" @default.
• W4285288146 creator A5051633336 @default.
• W4285288146 date "2022-01-01" @default.
• W4285288146 modified "2023-10-17" @default.
• W4285288146 title "Cauchy problem for nonlocal diffusion equations modelling Lévy flights" @default.
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• W4285288146 doi "https://doi.org/10.14232/ejqtde.2022.1.18" @default.
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