Dynamical behaviors for analyzing the stability of glycolysis model using fractal–fractional derivative

One very useful tool for simulating the intricate feedback processes that take place in a biological system is the glycolysis model. The nonlinearity, stiffness, and parameter sensitivity of this system make it difficult to accurately predict its behavior. This article focuses on the stability analysis of fractal–fractional derivatives for glycolysis modeling of the biochemical system. The primary objective is to examine the criteria for existence and uniqueness using the fixed-point technique. The study explores the Hyers–Ulam stability results and discusses other significant findings for the proposed model, and also employs numerical schemes using the Lagrange interpolation polynomial method. Finally, simulated graphical representations for various fractal–fractional order values are generated, and the simulation results confirm the effectiveness and practical applicability of the theoretical findings.