The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system ...

In this paper, global adaptive finite-time control problems for two special classes of nonlinear control systems with parametric uncertainties are considered. A simple design approach is given based on Lyapunov function and homogeneity. The feedback laws can be constructed in the form with fractional powers as shown in the design examples.

In this paper, we establish a local stable manifold theorem near a hyperbolic equilibrium point for planar fractional differential equations. The construction of this stable manifold is based on the associated Lyapunov-Perron operator. An example is provided to illustrate the result.

*Correspondence: [email protected] 2Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China Full list of author information is available at the end of the article Abstract By constructing two scaling matrices, i.e., a function matrix (t) and a constant matrix W which is not equal to the identity matrix, a kind ofW – (t) synchronization between fractional-order an...

Lyapunov stability of fractional differential equations is addressed in this paper. The key concept is the frequency distributed fractional integrator model, which is the basis for a global state space model of FDEs. Two approaches are presented: the direct one is intuitive but it leads to a large dimension parametric problem while the indirect one, which is based on the continuous frequency di...

1 *Assistant Professor, Electrical and Computer Engineering Department, Kharazmi University, Tehran, Iran,: [email protected], 2 .Associated Professor, Faculty of Electrical Engineering, Tarbiat Modares University, Tehran, Iran. 3 .Assistant Professor, Faculty of Electrical Engineering, Tarbiat Modares University, Tehran, Iran Abstract Non-fragile H ∞ observer design is the main problem of th...

In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signa...

In this work, we obtain a Lyapunov-type inequality for a\ fractional differential equation involving Caputo derivatives of higher order and subject to nonlocal boundary conditions. An application eigenvalue problems is also given.