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The Stochastic Schrödinger–Hirota equation plays a crucial role in describing the quantum behavior of physical systems under the influence of stochastic processes. In this manuscript, we present a comprehensive study on the exact solutions of the Stochastic Schrödinger–Hirota equation employing a novel approach, namely the variable coefficient third-degree generalized Abel equation method. This method extends the applicability of Abel's equation with variable coefficients, providing a powerful tool for solving complex nonlinear equations arising in stochastic quantum mechanics. The manuscript findings hold potential implications for diverse fields, including quantum physics, statistical mechanics, and mathematical physics. Moreover, the developed methodology could find applications in solving other nonlinear equations arising in different branches of science and engineering, broadening its scope and impact. • The paper introduces a novel approach, the variable coefficient third-degree generalized Abel equation method, to comprehensively study and solve the Stochastic Schrödinger–Hirota equation. • This innovative methodology extends the applicability of Abel's equation with variable coefficients, providing a powerful tool for addressing complex nonlinear equations in the realm of stochastic quantum mechanics. • The developed methodology introduces a systematic and effective approach that could enhance our ability to tackle complex nonlinear equations across various scientific disciplines. [ABSTRACT FROM AUTHOR]