In this paper, fractional Lyapunov functions for epidemic models are introduced and the concept of Mittag-Leffler stability is applied. The global model at an equilibrium state established.

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate stability with respect to motion changes at fractional changes of variables. Note that dynamical systems, which are unstable ”in sense of Lyapunov”, can be stable w...

Abstract: According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and ...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...

Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within th...

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...