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In this research, we use the homotopy perturbation method (HPM) combined with the Elzaki transform to investigate the fractional Biswas–Milovic equation (BME) within the framework of the Caputo operator. The fractional BME is a significant mathematical model with applications in various scientific and engineering fields, including physics, biology, and chemistry. However, its fractional nature introduces analytical complexities. By integrating the HPM with the Elzaki transform, we aim to provide an effective approach for obtaining accurate solutions to this equation. The combination of these mathematical techniques allows us to explore the behavior of the fractional BME in a comprehensive manner. The research outcomes are supported by numerical results and comparisons, demonstrating the reliability and efficiency of the proposed methodology. This study contributes to advancing the tools for solving fractional equations and enhances our understanding of the intricate dynamics described by the fractional BME.

A homotopy perturbation method with Elzaki transformation for solving the fractional Biswas–Milovic model