The Fornax galaxy cluster was observed with the High Energy Stereoscopic System (H.E.S.S.) for a total live time of 14.5 hours, searching for very-high-energy (VHE, E>100 GeV) gamma-rays from dark matter (DM) annihilation. No significant signal was found in searches for point-like and extended emissions. Using several models of the DM density distribution, upper limits on the DM velocity-weighted annihilation cross-section <sigma v> as a function of the DM particle mass are derived. Constraints are derived for different DM particle models, such as those arising from Kaluza-Klein and supersymmetric models. Various annihilation final states are considered. Possible enhancements of the DM annihilation gamma-ray flux, due to DM substructures of the DM host halo, or from the Sommerfeld effect, are studied. Additional gamma-ray contributions from internal bremsstrahlung and inverse Compton radiation are also discussed. For a DM particle mass of 1 TeV, the exclusion limits at 95% of confidence level reach values of <sigma v> ~ 10^-23cm^3s^-1, depending on the DM particle model and halo properties. Additional contribution from DM substructures can improve the upper limits on <sigma v> by more than two orders of magnitude. At masses around 4.5 TeV, the enhancement by substructures and the Sommerfeld resonance effect results in a velocity-weighted annihilation cross-section upper limit at the level of <sigma v> ~ 10^-26cm^3s^-1.
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