Fractal–fractional approach to stability in enzyme kinetics: A mathematical model perspective

Chemical kinetics is the study of the rates of chemical reactions and the mechanisms by which they occur. This field is critical for optimizing industrial processes, such as fertilizer and pharmaceutical production, by increasing efficiency and yield. In environmental science, understanding reaction rates is crucial for modeling pollution dynamics and assessing environmental impacts. In biochemistry, chemical kinetics reveals the intricacies of cellular processes, aiding in the understanding of disease mechanisms and the development of new drugs. This article focuses on the stability analysis of fractal–fractional derivatives for enzyme kinetics. The primary objective is to examine the criteria for existence and uniqueness using the fixed-point technique. The study explores Hyers–Ulam stability results and discusses other significant findings for the proposed model and also employs numerical schemes using the Lagrange polynomial interpolation method. Finally, generate simulated graphical representations for various fractal–fractional order values, and the simulation results confirm the effectiveness and practical applicability of the theoretical findings.