Relative controllability of conformable delay differential systems with linear parts defined by permutable matrices

We study relative controllability of linear and nonlinear conformable delay differential systems with parts defined by permutable matrices. By using a notion Grammian matrix, we give sufficient necessary condition to examine that controlled is relatively controllable. Thereafter, construct suitable control function for system, which admits us adopt the framework fixed point methods investigate same issue. More precisely, apply Krassnoselskii?s theorem derive result. Finally, two examples are presented illustrate our theoretical results help computing desired functions inverse matrix as well.