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
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 110p-124p
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.
MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo
on the occasion of his 80th anniversary