This paper makes an accurate fractional model of the existing non-linear systems using fractional order theory and various intelligent optimization methods and proposes a novel method to identify time-varying parameters of the fractional non-linear system offline and online. More accurate mathematical model of the proposed system was made by applying approximated fractional derivative into the state space model of the classical non-linear system. The initial parameter values of the proposed non-linear fractional system were identified offline by using hybrid particle swarm optimization-genetic algorithm method that is a combination of particle swarm optimization(PSO) and genetic algorithm(GA) that are typical intelligent optimization methods. The time-varying parameters of the non-linear fractional order systems were identified online in real-time by using the output error technique and the recursive least square method. In order to verify the efficiency of the proposed identification technique, we made a simulation experiment for offline and online identification of the time-varying parameters in the existing nonlinear fractional Lorentz system and nonlinear fractional lithium-ion battery system. Simulation results show that the proposed novel identification method can be effectively used for offline and online parameter identification of many complicated non-linear fractional order systems in practice.