In this paper, we study nonlinear differential equations with Caputo fractional derivatives with respect to other functions and impulses. The main characteristic of the impulses is that the time between two consecutive impulsive moments is defined by random variables. These random variables are independent. As the distribution of these random variables is very important, we consider the Erlang distribution. It generalizes the exponential distribution, which is very appropriate for describing the time between the appearance of two consecutive events. We describe a detailed solution to the studied problem, which is a stochastic process. We define the p-exponential stability of the solutions and obtain sufficient conditions. The study is based on the application of appropriate Lyapunov functions. The obtained sufficient conditions depend not only on the nonlinear function and impulsive functions, but also on the function used in the fractional derivative. The obtained results are illustrated using some examples.

The widespread application of plain S235JR steel across various industries often involves its exposure to degradative conditions, such as the organic acid concentrations typically found in various foodstuffs. This study investigates the corrosion behavior of S235JR steel immersed in several common beverages. The corrosion of steel S235JR was evaluated by gravimetric and electrochemical study. Statistical modeling via multiple linear regression and ANOVA was utilized to verify the experimental dataset. Based on the results, the highest early-stage corrosion occurs in coffee and tomato juice, though apple cider vinegar stands out for its steadily intensifying corrosive effect over the immersion period. Conversely, the presence of citric acid in lemon and orange juices appears to act as an inhibitor, leading to the lowest observed corrosion rates. The strong correlation between electrochemical parameters ($I_{corr}$ and $E_{ocp}$) and physical mass loss confirms that the chemical nature of each beverage significantly governs the corrosion kinetics of S235JR.