This study explores the motivational factors behind alcohol consumption and its societal impacts. It identifies key reasons for drinking, such as improving sociability, boosting confidence, coping with challenges, participating in rituals, and seeking detoxification. The study highlights the substantial societal harm caused by the use of alcohol and drugs, with a particular emphasis on the increase in sexual violence, both within and outside families, as a result of impaired behavior. In this work, we present a newly developed mathematical model within the Caputo fractional framework, designed to reflect the lifestyle and behaviors of individuals in the alcohol model. We analyze the existence and uniqueness of solutions using the Lipschitz growth condition and fixed point theory. In addition, we explore equilibrium points, compute basic reproduction numbers, and explore the Hyers–Ulam stability of the alcohol model. Finally, we develop a numerical scheme for computational analysis of the proposed fractional model.

The implications of the Schrödinger equation is profound, revealing the wave-particle duality of matter, the concept of superposition, and the probabilistic nature of quantum measurements. Its solutions provide critical insights into the behavior of atoms, molecules, and subatomic particles, forming the foundation for much of modern physics and technology. This article is concerned with the existence and uniqueness of solutions for Schrödinger equation that involve fractional differential equations using the Caputo method with initial conditions, as well as exploring the Hyers-Ulam stability of the Schrödinger equation was investigated when the relevant system has a potential well of finite depth using a fixed-point approach. Finally, we present the graphical representation for the Schrödinger equation related to the harmonic oscillator.