The bioreactor model’s coupled nonlinear initial value problem, which describes the concentration of nutrients and bacteria in a closed chamber, is examined using a structural derivative approach. Two distinct structural functions are used: one that results in a singular coefficient and the other in a non-singular coefficient to the classical derivative. The numerical simulations demonstrate that the structural function governing non-singular derivatives exhibits smooth variations in concentration profile. Furthermore, evaluating the anomalies over time using the fractal parameter is simple. Compared to convolution-based fractional derivative model, the suggested non-integer derivative approach is simpler to use and analyse.