International Journal of Differential Equations

On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis

D. Goos, G. Reyero, S. Roscani, and E. Santillan Marcus

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We consider the time-fractional derivative in the Caputo sense of order α(0, 1). Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in R+, two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when α1 of the respective solutions is analyzed, recovering the solutions of the classical boundary-value problems when α = 1, and the fractional diffusion equation becomes the heat equation.

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Int. J. Differ. Equ., Volume 2015 (2015), Article ID 439419, 14 pages.

Received: 10 July 2015
Accepted: 31 August 2015
First available in Project Euclid: 20 January 2017

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Goos, D.; Reyero, G.; Roscani, S.; Santillan Marcus, E. On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis. Int. J. Differ. Equ. 2015 (2015), Article ID 439419, 14 pages. doi:10.1155/2015/439419.

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