<p>Fractional-order (FO) systems have gained prominence in scientific and engineering applications due to their enhanced modeling capabilities for real-world dynamics. However, correctly incorporating FO elements in analog circuits remains a considerable challenge. Existing fitting-based analog models, particularly those based on partial fraction decomposition, have low precision and are frequently unsuitable for practical applications. To address this, we propose a modified fractional-order low-pass Butterworth filter (MFOLBF) based on an integer-order continuous-time transfer function. The filter coefficients are optimized using Entropy-based Sunflower Optimization (ESFO), a metaheuristic method inspired by nature that addresses complex, nonlinear, and multidimensional design spaces. By using third-order rational approximations, ESFO effectively reduces the difference between the ideal and estimated filter responses. The result is a set of optimized coefficients that closely match the magnitude characteristics of the ideal MFOLBF. This method enhances the accuracy and practicality of fractional-order filter designs, offering a reliable option for situations that require high-performance analog signal processing.</p>