BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Fractional Calculus and Applied Analysis >
2011 >

Please use this identifier to cite or link to this item:

Title: Maximum Principle and Its Application for the Time-Fractional Diffusion Equations
Authors: Luchko, Yury
Keywords: Time-Fractional Diffusion Equation
Time-Fractional Multiterm Diffusion Equation
Time-Fractional Diffusion Equation of Distributed Order
Extremum Principle
Caputo Fractional Derivative
Generalized Riemann-Liouville Fractional Derivative
Initial-Boundary-Value Problems
Maximum Principle
Uniqueness 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
ISSN: 1311-0454
Appears in Collections:2011

Files in This Item:

File Description SizeFormat
fcaa-vol14-num1-2011-110p-124p.pdf226.41 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License