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This research aims to contribute to depolluting textile effluents and limiting their toxicity to the health and environment. In this framework, x%Cu@FbHAp (copper-impregnated fishbone hydroxyapatite) catalyst was characterized by BET, XRD, pHpzc, FTIR, and SEM-EDX to be applied in the catalytic wet peroxide oxidation (CWPO) of the Brilliant Green (BG) cationic dye and the Methyl Orange (MeO) anionic dye. Contact of the x%Cu@FbHAp catalyst with hydrogen peroxide promotes free radicals responsible for oxidation rates of 91.5 % and 81.43 % for BG and MeO respectively under the following operating conditions: dye concentration (100 mg/L), catalyst dose (1 g/L), H2O2 concentration (0.049 M), copper content (1 %Cu@FbHAp), temperature (20 °C) and pH (6.8). These decolorization rates were further improved by Box Behnken response surface methodology applied to 1 %Cu@FbHAp to achieve 98.56 % and 99.28 % for BG and MeO respectively at 60 mg/L dye concentration, 0.0735 M H2O2 concentration, and 2 g/L catalyst dose. The CWPO process mechanism is essentially based on the action of the 1 % Cu@FbHAp catalyst for hydrogen peroxide decomposition into reactive hydroxyl radicals that attack the chemical bonds of organic dyes, leading to their decolorization. DFT calculations show that BG is more reactive than MeO, with a lower energy gap, higher electrophilicity, and lower chemical hardness. However, its ability to accept electrons is slightly lower than MeO’s. The high regeneration capacity (several cycles) and low cost ($0.062 L-1 estimated by Ishikawa approach) of hydroxyapatite-based catalytic materials are highly cost-effective for industrial applications and ecologically beneficial.