Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1685

 Title: Maximum Principle and Its Application for the Time-Fractional Diffusion Equations Authors: Luchko, Yury Keywords: Time-Fractional Diffusion EquationTime-Fractional Multiterm Diffusion EquationTime-Fractional Diffusion Equation of Distributed OrderExtremum PrincipleCaputo Fractional DerivativeGeneralized Riemann-Liouville Fractional DerivativeInitial-Boundary-Value ProblemsMaximum PrincipleUniqueness Results Issue Date: 2011 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 110p-124p Abstract: In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative, the Caputo fractional derivative is shown to possess a suitable generalization of the extremum principle well-known for ordinary derivative. As an application, the maximum principle is used to get some a priori estimates for solutions of initial-boundary-value problems for the generalized time-fractional diffusion equations and then to prove uniqueness of their solutions. Description: MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary URI: http://hdl.handle.net/10525/1685 ISSN: 1311-0454 Appears in Collections: 2011

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