# Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

Fractional Calculus and Applied Analysis (2011)

- Volume: 14, Issue: 1, page 110-124
- ISSN: 1311-0454

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topLuchko, Yury. "Maximum Principle and Its Application for the Time-Fractional Diffusion Equations." Fractional Calculus and Applied Analysis 14.1 (2011): 110-124. <http://eudml.org/doc/219664>.

@article{Luchko2011,

abstract = {MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo
on the occasion of his 80th anniversaryIn 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.},

author = {Luchko, Yury},

journal = {Fractional Calculus and Applied Analysis},

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; time-fractional diffusion equation; time-fractional multi-term 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},

language = {eng},

number = {1},

pages = {110-124},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Maximum Principle and Its Application for the Time-Fractional Diffusion Equations},

url = {http://eudml.org/doc/219664},

volume = {14},

year = {2011},

}

TY - JOUR

AU - Luchko, Yury

TI - Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

JO - Fractional Calculus and Applied Analysis

PY - 2011

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 14

IS - 1

SP - 110

EP - 124

AB - MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo
on the occasion of his 80th anniversaryIn 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.

LA - eng

KW - 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; time-fractional diffusion equation; time-fractional multi-term 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

UR - http://eudml.org/doc/219664

ER -

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