A comprehensive study of a feedback control problem with a state-dependent implicit pantograph equation of Chandrasekhar type

In this research, we investigate the existence of at least one continuous solution of a problem with feedback control involving implicit pantograph equations of the Chandrasekhar type with state-dependent delay. In addition, we examine the possibility of the uniqueness of the solution under suitable assumptions. Furthermore, we analyze the problem's Hyers-Ulam stability and the continuous dependency of the unique solution on the original data and the parameter. Moreover, we look into this problem in the absence of feedback control. We provided a few instances to indicate our findings.