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In this paper, a fractional-order robust adaptive intelligent controller (FRAIC) is designed for a class of chaotic fractional order systems with uncertainty, external disturbances and unknown time-varying input time delay. The time delay is considered both constant and time varying. Due to changes in the equilibrium point, adaptive control is used to update the system's momentary information and the intelligent controller is used to estimate the uncertainties and disturbances and non-linearities of the system according to the momentary information obtained. The sliding mode control, which provides closed loop asymptotic stability in the system despite the uncertainties and disturbances, is used as a robust controller. Using the Lyapunov theorem and Barbalat's Lemma, the asymptotic stability of a chaotic fractional order system with input delay and uncertainty as well as external disturbance is proved by designed controller. Finally, using the simulation results of financial as well as supply and demand systems, the performance of designed controller would be examined.

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The modeling of high frequency electromagnetic transients and the simulation of the voltage and the current distribution in the multi-winding traction transformer's windings due to these transient waves are very important. In the present article, in addition of presenting finite element models, the coupled field-circuit approach is proposed for the modeling of high frequency electromagnetic transients in a multi-winding traction transformer. The proposed method uses two-dimensional finite element models coupled with an external circuit to model the electromagnetic transient behavior of the multi-winding traction transformer. Afterwards, the results of the presented method have been compared with the results obtained from a complete three-dimensional finite element model as well as the detail model's results and the results are validated. Finally, the validated high-frequency model has been used to study the impulse response of the transformer. As shown, the proposed approach is a simple and fast method, and also has good accuracy in modeling of the impulse voltage distribution in the multi-winding traction transformer's windings.