Geodesic
Maximum Principle and Its Application for the Time-Fractional Diffusion Equations
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 110-124.

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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.
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 
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     author = {Luchko, Yury},
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Luchko, Yury. Maximum Principle and Its Application for the Time-Fractional Diffusion Equations. Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 110-124. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a6/