Analysis of school bullying menace incorporating family education: a mathematical modeling approach

School bullying is a severe social problem that has an unfavorable impact on students development and behavior. Based on family education and students memory of having been bullied or witnessed bullying, this work established a mathematical model for analyzing school bullying dynamics. By employing the Caputo fractional derivative, the model incorporates students' memory in the interactional patterns of bullying, which provides for improved emulation of the impacts of previous episodes on future behaviors. An Adams-Bashforth method numerical scheme is presented, offering a robust approach for scenario simulations under the Caputo fractional operator. Scenario simulations shows the impact of family education on the prevalence and dynamics of school bullying. It is noticed that the behavior of students who lack and with family education and not involving bullying under different values of fractional order. The trajectory changes with the fractional order, suggesting that the system's sensitivity to initial conditions or recent changes decreases as fractional order reduce from the normal dynamics (integer order). Essentially, a lower fractional order makes the system less reactive to short-term fluctuations and more stable.