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The precise estimation of fracture initiation pressure is crucial for the effective implementation of slotting-directional hydraulic fracturing methods in coal seams. Nonetheless, current models fail to account for the impact of the morphology of the slotted borehole and the anisotropy of coal. To address this issue, a three-dimensional model was created in this study, which simplified the slotted borehole as an elliptical medium and the coal as an orthotropic medium. Laboratory experiments were conducted to validate the model, and the findings regarding the changes in fracture initiation pressure and deflection angle due to various factors were presented. The calculated outcomes of the proposed model align with the observed pattern of the experimental results, and the numerical discrepancy falls within the acceptable range of 7%, showcasing the precision of the proposed model. A rise in the horizontal stress difference and a decrease in the depth of the slots will result in an elevation of the fracture initiation pressure and deflection angle. In addition, the slotting angle will impact the distribution pattern of the fracture initiation pressure and deflection angle, underscoring the significance of these factors in the hydraulic fracturing of slotted boreholes.