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

International Journal of Differential Equations, 2015, vol. 2015, 1-14

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:439419

DOI: 10.1155/2015/439419

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