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The holographic complexity conjectures are considered in aEinstein-Maxwell-Dilaton gravity, by using the "Complexity-Volume" proposal.Specifically, we calculate the growth rate of complexity for an eternal chargedAdS-dilaton black holes with fixed and dynamical boundaries respectively. Thedynamical boundary is achieved by introducing a moving self-graviting brane onwhich the induced metric has an exact FLRW form. In case of fixed AdS boundary,there exists a bound for evolution of growth rate on late time, while thisbound will become larger as the dilaton coupling constant $\alpha$ increases.In large $\alpha$ limit, we analytically prove that this bound is a finitevalue which is proportional to the black hole mass. In case of dynamicalboundary, namely the brane-bulk system, the growth rate decreases monotonouslyon late time, after reaching a maximum value at a certain time. We find thatthe evolution of growth rate for brane-bulk system on late time is dominated bythe velocity of the moving brane. We guess this result is model-independent.

Holographic complexity growth for a charged AdS-dilaton black holes with fixed and dynamical boundary respectively