## International Journal of Differential Equations

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

#### Abstract

We consider the time-fractional derivative in the Caputo sense of order $\alpha \in (0, 1)$. Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in ${\mathbb{R}}^{+}$, two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when $\alpha ↗1$ 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.

#### Article information

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

Dates
Accepted: 31 August 2015
First available in Project Euclid: 20 January 2017

https://projecteuclid.org/euclid.ijde/1484881444

Digital Object Identifier
doi:10.1155/2015/439419

Mathematical Reviews number (MathSciNet)
MR3413056

Zentralblatt MATH identifier
1336.35358

#### Citation

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. https://projecteuclid.org/euclid.ijde/1484881444

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