Abstract: Aiming at the problem of accurate modeling and efficient control of complex dynamic systems, we discussed  the optimal control model of nonlocal nonlinear equations with 0<s≤1 order fractional Laplacian operator. Firstly, the existence and uniqueness of the solution to the equation were proved by using Schauder fixed point theorem and Gronwall inequality. Secondly,  the boundedness of the solution to the equation was established by introducing the measure theory. Finally, the existence of the optimal control function solution to the equation was proved by using the weak lower semicontinuity of the cost functional.

Key words:  , nonlocal nonlinear fractional order equation, optimal control, boundedness