Cauchy problem for general time fractional diffusion equation
2020 ◽
Vol 23
(5)
◽
pp. 1545-1559
Keyword(s):
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.
2017 ◽
Vol 50
(30)
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pp. 305203
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2013 ◽
Vol 10
(02)
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pp. 1341001
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2014 ◽
Vol 40
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pp. 128-137
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2019 ◽
Vol 77
(5)
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pp. 1408-1422
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2022 ◽
Vol 507
(1)
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pp. 125741
2019 ◽
Vol 34
(3)
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pp. 284-308
2021 ◽
Vol 386
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pp. 113213