This paper presents a new advancement in modeling chemically controlled reactions using a dynamical system and analyzes the dependence of its solution on initial conditions through mathematical techniques involving fractional orders. The authors use a fixed-point approach to derive the existence and uniqueness theorem of the proposed model. They also demonstrate the stability of the fractional model's chemical kinetics using the Hyers-Ulam stability condition. A numerical simulation is conducted to verify the conclusions. The paper concludes with demonstrative examples. Chemical kinetics is the study of reaction rates and the factors influencing them. It is essential for various applications, including industrial processes, environmental chemistry, and drug development. The paper discusses fundamental principles of chemical reaction speeds and reaction mechanisms, including reaction rate laws, activation energy, and factors affecting reaction rates such as temperature, concentration, catalysts, and surface area. It also explores the role of enzyme kinetics in driving biological phenomena. The paper highlights the importance of fractional-order derivatives in understanding the dynamical behavior of physical systems. Fractional differential equations are a significant area of research, offering a more realistic understanding of natural phenomena. The paper discusses various applications of fractional calculus, including conservation laws, reaction-diffusion models, Legendre functions, oscillatory systems, non-local and nonsingular kernels, disease spread, Hepatitis C, vector-borne diseases, SARS-CoV-2, and shale gas production prediction. It also examines the application of fractional differential equations in modeling non-local effects and memory-dependent behaviors. The paper references several studies that have used fractional calculus in modeling biological and medical systems.This paper presents a new advancement in modeling chemically controlled reactions using a dynamical system and analyzes the dependence of its solution on initial conditions through mathematical techniques involving fractional orders. The authors use a fixed-point approach to derive the existence and uniqueness theorem of the proposed model. They also demonstrate the stability of the fractional model's chemical kinetics using the Hyers-Ulam stability condition. A numerical simulation is conducted to verify the conclusions. The paper concludes with demonstrative examples. Chemical kinetics is the study of reaction rates and the factors influencing them. It is essential for various applications, including industrial processes, environmental chemistry, and drug development. The paper discusses fundamental principles of chemical reaction speeds and reaction mechanisms, including reaction rate laws, activation energy, and factors affecting reaction rates such as temperature, concentration, catalysts, and surface area. It also explores the role of enzyme kinetics in driving biological phenomena. The paper highlights the importance of fractional-order derivatives in understanding the dynamical behavior of physical systems. Fractional differential equations are a significant area of research, offering a more realistic understanding of natural phenomena. The paper discusses various applications of fractional calculus, including conservation laws, reaction-diffusion models, Legendre functions, oscillatory systems, non-local and nonsingular kernels, disease spread, Hepatitis C, vector-borne diseases, SARS-CoV-2, and shale gas production prediction. It also examines the application of fractional differential equations in modeling non-local effects and memory-dependent behaviors. The paper references several studies that have used fractional calculus in modeling biological and medical systems.