We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract resul...

We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant FO-LTI systems. To determine the control parameters, one needs only a little knowledg...

In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order (SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbau...

This study constructs a novel four-dimensional fractional-order chaotic system. It verifies chaotic nonlinear dynamic behaviors and physical reliability by numerical simulation and hardware circuit design. For a class of parameter uncertainty fractional different-lags ( i ) chaotic systems, the authors design a time-delayed ( ) synchronization controllers and parameter adaptive laws. It proves ...

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

In this paper, the fractional-order chaotic system form of a four-dimensional with cross-product nonlinearities is introduced. The stability equilibrium points and then feedback control design to achieve goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, largest Lyapunov exponent are presented. Finally, global Mittag–Leffler attra...

this paper proposes an optimized control policy over type one diabetes. type one diabetes is taken into consideration as a nonlinear model (augmented minimal model), which is implemented in matlab-simulink. this model is developed in consideration of the patient's conditions. there are some uncertainties in the regarded model due to factors such as blood glucose concentration, daily meals ...