in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stab...

A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for ...

In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulati...

This paper addresses the problem of the fractional sliding mode control (FSMC) for a MEMS optical switch. The proposed scheme utilizes a fractional sliding surface to describe dynamic behavior of the system in the sliding mode stage. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed sliding surface displays better transient per...

This paper addresses the problem of the fractional sliding mode control (FSMC) for a MEMS optical switch. The proposed scheme utilizes a fractional sliding surface to describe dynamic behavior of the system in the sliding mode stage. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed sliding surface displays better transient per...

Abstract: By using a linear feedback control technique, we propose a chaos synchronization scheme for nonlinear fractional discrete dynamical systems. Then, we construct a novel 1-D fractional discrete income change system and a kind of novel 3-D fractional discrete system. By means of the stability principles of Caputo-like fractional discrete systems, we lastly design a controller to achieve ...

The concept of a fractional derivative is not at all intuitive, starting with having clear geometrical interpretation. Many different definitions have appeared, to the point that need for order has arisen in field. diversity potential applications even more overwhelming. When modeling problem, one must think carefully about what introduction derivatives model can provide was already adequately ...