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International Journal of Differential Equations
Volume 2015, Article ID 439419, 14 pages
http://dx.doi.org/10.1155/2015/439419
Research Article

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

1Departamento de Matemática, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, S2000BTP Rosario, Argentina
2CONICET, Departamento de Matemática, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, S2000BTP Rosario, Argentina
3Departamento de Matemática, FCE, Universidad Austral, Paraguay 1950, S2000FZF Rosario, Argentina

Received 10 July 2015; Accepted 31 August 2015

Academic Editor: Nasser-Eddine Tatar

Copyright © 2015 D. Goos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the time-fractional derivative in the Caputo sense of order . Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in , two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when 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.