<p>This paper introduces a novel method for designing both IIR and FIR fractional delay filters, which introduce delays that are fractions of the sampling period. The method utilizes a biquadratic function and a closed-form approximation of the fractional delay operator z^−m to closely match the ideal frequency response at a specific frequency. The approach first approximates the analog fractional order operator s^±m using the El-Khazali&#xa0;method and converts it to a digital design via the Backward-Euler transformation. Then, it approximates z^−m using a composite function rule and a digital El-Khazali approximation. By truncating the digital biquadratic function, a closed-form FIR fractional delay filter is derived. Numerical examples demonstrate this approach’s effectiveness and suitability for real-time applications due to its simplicity.</p>