Maximum principle for the generalized time-fractional diffusion equation

In the paper, a maximum principle for the generalized time-fractional diffusion equation over an open bounded domain G x (0. T). G subset of R-n is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Caputo-Dzherbashyan fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the generalized time-fractional diffusion equation possesses at most one classical solution and this Solution continuously depends on the initial and boundary conditions. (c) 2008 Elsevier Inc. All rights reserved.