Fractional order control-a tutorial
Many real dynamic systems are better characterized using a non-integer order dynamic
model based on fractional calculus or, differentiation or integration of non-integer order …
model based on fractional calculus or, differentiation or integration of non-integer order …
A survey on the stability of fractional differential equations: Dedicated to Prof. YS Chen on the Occasion of his 80th Birthday
CP Li, FR Zhang - The European Physical Journal Special Topics, 2011 - Springer
Recently, fractional calculus has attracted much attention since it plays an important role in
many fields of science and engineering. Especially, the study on stability of fractional …
many fields of science and engineering. Especially, the study on stability of fractional …
Fractal system as represented by singularity function
A Charef, HH Sun, YY Tsao… - IEEE Transactions on …, 1992 - ieeexplore.ieee.org
A fractional slope on the log log Bode plot has been observed in characterizing a certain
type of physical phenomenon and has been called the fractal system or the fractional power …
type of physical phenomenon and has been called the fractal system or the fractional power …
Chaos in a fractional order Chua's system
TT Hartley, CF Lorenzo… - IEEE Transactions on …, 1995 - ieeexplore.ieee.org
This brief studies the effects of fractional dynamics in chaotic systems. In particular, Chua's
system is modified to include fractional order elements. By varying the total system order …
system is modified to include fractional order elements. By varying the total system order …
Remarks on fractional derivatives
In this paper, we further discuss the properties of three kinds of fractional derivatives: the
Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative …
Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative …
Chaos and hyperchaos in the fractional-order Rössler equations
The dynamics of fractional-order systems have attracted increasing attentions in recent
years. In this paper, we numerically study the chaotic behaviors in the fractional-order …
years. In this paper, we numerically study the chaotic behaviors in the fractional-order …
Chaos in the fractional order Chen system and its control
In this letter, we study the chaotic behaviors in the fractional order Chen system. We found
that chaos exists in the fractional order Chen system with order less than 3. The lowest order …
that chaos exists in the fractional order Chen system with order less than 3. The lowest order …
Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays
R Rakkiyappan, J Cao… - IEEE Transactions on …, 2014 - ieeexplore.ieee.org
This paper deals with the problem of existence and uniform stability analysis of fractional-
order complex-valued neural networks with constant time delays. Complex-valued recurrent …
order complex-valued neural networks with constant time delays. Complex-valued recurrent …
A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application
Memelements play an important part in the design of high density memory systems and low
power memory. In this paper, we created a novel fractional-order chaotic circuit with a …
power memory. In this paper, we created a novel fractional-order chaotic circuit with a …
Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization
AA Elsadany, AE Matouk - Journal of Applied Mathematics and Computing, 2015 - Springer
In this work, we study the dynamical behaviors of fractional-order Lotka–Volterra predator–
prey system and its discretized counterpart. It is shown that the discretized system exhibits …
prey system and its discretized counterpart. It is shown that the discretized system exhibits …