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2015 On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis
D. Goos, G. Reyero, S. Roscani, E. Santillan Marcus
Int. J. Differ. Equ. 2015: 1-14 (2015). DOI: 10.1155/2015/439419

Abstract

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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D. Goos. G. Reyero. S. Roscani. E. Santillan Marcus. "On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis." Int. J. Differ. Equ. 2015 1 - 14, 2015. https://doi.org/10.1155/2015/439419

Information

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

zbMATH: 1336.35358
MathSciNet: MR3413056
Digital Object Identifier: 10.1155/2015/439419

Rights: Copyright © 2015 Hindawi

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