In this paper, four control structures are provided for continuous ctirred-tank reactor (CSTR) system's fractional/integer order proportional integral derivative neural network controllers. The revised neural network weights and the controller's parameters are optimized using the optimization technique called ant colony optimization (ACO). The proposed controllers' resistance to changes in the initial state, outside disturbances, and parameter modifications is also tested. The fractional order proportional integral derivative neural network controllers provide the best assurance and also enhance the system's robustness to changes in the initial state, external disturbances, and parameter variations, according to the results of MATLAB code.The fractional order proportional integral derivative neural network controller1(FOPIDNNC1) is the best structure among all those with the minimum cost function equal to 0.011588 for the set-point variations, 0.015325 for uncertainty parameter, 0.018274 for disturbances rejection, and the best structure fractional order proportional integral derivative neural network controller3 (FOPIDNNC3) among all those with the minimum cost function equal to 0.008733 for tracking.