On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis
2015 ◽
Vol 2015
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pp. 1-14
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Keyword(s):
The Real
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We consider the time-fractional derivative in the Caputo sense of orderα∈(0, 1). Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function inR+, two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit whenα↗1of the respective solutions is analyzed, recovering the solutions of the classical boundary-value problems whenα= 1, and the fractional diffusion equation becomes the heat equation.
2012 ◽
Vol 15
(1)
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2011 ◽
Vol 374
(2)
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pp. 538-548
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2016 ◽
Vol 19
(3)
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1994 ◽
Vol 15
(3)
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pp. 267-273
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2018 ◽
Vol 7
(4)
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pp. 669-682
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2014 ◽
Vol 78
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pp. 95-111
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