Representation and finite time stability of solution and relative controllability of conformable type oscillating systems

摘要

In this paper, we firstly introduce the concept of conformable matrix sine and cosine functions, which help us to seek explicit formula of solutions to a conformable type linear oscillating system by using the variation of constants method. Secondly, we establish some sufficient conditions to guarantee the finite time stability results and give sufficient and necessary conditions to examine that a linear conformable system is relatively controllable. Further, we apply fixed point theorem to prove relatively controllable result for a semilinear conformable system. Finally, examples are presented to illustrate the validity of the main theorems.