A study on the finite time stability and controllability of time delay fractional model

The mainspring of this analytical study is to implement the idea of delayed argument cosine and sine conformable matrices to interpret the stability bounds of conformable type fractional operator over finite time period using modified integral form of Gronwall’s inequality. Further, we establish the conformable Grammian matrices in-terms of sine function to analyze the controllability results. The main inception is to first consider the linear controllability result of our defined system and to a greater extent, fixed point techniques along with the properties of Bochner-integral and inner product spaces are implemented to verify the controllability results of the nonlinear system. The theoretical study is graphically visualized using matlab software.