Chemical processes are vital in various industries but are often complex and nonlinear, making accurate modeling essential. Traditional linear approaches struggle with dynamic behaviour and changing conditions. This paper explores the advantages of the new theory of fractional neural networks (FNNs), focusing on applying fractional activation functions for continuous stirred tank reactor (CSTR) modeling. The proposed approach offers promising solutions for real-time modeling of a CSTR. Various numerical analyses demonstrate the robustness of FNNs in handling data reduction, achieving better generalization, and sensitivity to noise, which is crucial for real-world applications. The identification process is more generalized and can enhance adaptability and improve industrial plant management efficiency. This research contributes to the growing field of real-time modeling, highlighting its potential to address the complexities in chemical processes.