*Correspondence: [email protected] 1School of Mathematical Sciences, Anhui University, Hefei, 230039, China 2School of Mathematics, Hefei University of Technology, Hefei, 230009, China Abstract In this paper, we investigate the stability of a class of nonlinear fractional neutral systems. We extend the Lyapunov-Krasovskii approach to nonlinear fractional neutral systems. Necessary and sufficient ...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the quadratic stability. Some examples are given to show the applicability and effectiveness of the proposed theory.

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach....

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach....

Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x (α) (t) = f (t, x(t)) + t t 0 K(t, s, x(s))ds, 0 < α ≤ 1, with the initial condition x (α−1) (t 0) = x 0 , have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.

This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractionalorder differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable control...