Lie symmetry, chaos optimal control in non-linear fractional-order diabetes mellitus, human immunodeficiency virus, migraine Parkinson's diseases models: using evolutionary algorithms.

The purpose of this article is to investigate the optimal control of nonlinear fractional order chaotic models of diabetes mellitus, human immunodeficiency virus, migraine and Parkinson's diseases using genetic algorithms and particle swarm optimization. Mathematical chaotic models of nonlinear fractional order type of the above diseases were presented. Then optimal control for each of the models and numerical simulation was done using genetic algorithm and particle swarm optimization algorithm. The results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method. Very low values of MSE and RMSE errors indicate that the simulation is effective and efficient. Also, Lie symmetry was calculated for the proposed models and the results were presented.