scholarly journals 0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Yuting Li
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Three Dimensional ◽  
Financial System ◽  
Investment Incentive ◽  
Integer Order ◽  
System A ◽  
Weighted Integral ◽  
Test Algorithm ◽  
Predictor Corrector

A new integer-order chaotic financial system is extended by introducing a simple investment incentive into a three-dimensional chaotic financial system. A four-dimensional fractional-order chaotic financial system is presented by bringing fractional calculus into the new integer-order financial system. By using weighted integral thought, the fractional order derivative's economics meaning is given. The 0-1 test algorithm and the improved Adams-Bashforth-Moulton predictor-corrector scheme are employed to detect numerically the chaos in the proposed fractional order financial system.

Fractional-Order PID Controller of a Heating-Furnace System

2012 ◽  
Vol 490-495 ◽  
pp. 1145-1149 ◽  
Author(s):  
Yan Mei Wang ◽  
Yi Jie Liu ◽  
Rui Zhu ◽  
Yan Zhu Zhang
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Pid Control ◽  
Pid Controller ◽  
Control Method ◽  
Heating Furnace ◽  
Order Model ◽  
Integer Order ◽  
System A ◽  
Fractional Order Pid

This paper discusses the fractional-order controller of heating-furnace system, a new PID controller of heating-furnace system based on fractional calculus will be considered. Classical PID control method is also studied. Then, this paper presents the fractional-order PID control method based on integer-order model of heating-furnace system. Meanwhile, simulation study is done. Comparing the control methods and strategies of integer order model of the heating-furnace system, a conclusion is drawn that PID control based on fractional calculus is much more complex than that of integer order controller. Numerical simulations are used to illustrate the improvements of the proposed controller for the integer-order heating-furnace systems.

scholarly journals Mathematical modelling of the mass-spring-damper system - A fractional calculus approach

2012 ◽  
Vol 22 (5) ◽  
pp. 5-11 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Juan Rosales García ◽  
Jesus Bernal Alvarado ◽  
Manuel Guía
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Mathematical Modelling ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Time Derivative ◽  
System A ◽  
Fractional Differential ◽  
Mass Spring ◽  
Derivatives Of

In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter char­acterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

scholarly journals Absorptive Repetitive Filters with Operators of Generalized Fractional Calculus

2013 ◽  
Vol 13 (4) ◽  
pp. 42-53 ◽  
Author(s):  
Nina Nikolova ◽  
Emil Nikolov
Keyword(s):  
Comparative Analysis ◽  
Fractional Calculus ◽  
Control Systems ◽  
Fractional Order ◽  
Fractional Integration ◽  
Frequency Characteristics ◽  
Rational Approximations ◽  
Integer Order ◽  
New Class ◽  
Generalized Fractional Calculus

Abstract : An essentially new class of repetitive fractional disturbance absorptive filters in disturbances absorbing control systems is proposed in the paper. Systematization of the standard repetitive fractional disturbance absorptive filters of this class is suggested. They use rational approximations of the operators for fractional integration in the theory of fractional calculus. The paper discusses the possibilities for repetitive absorbing of the disturbances with integer order filters and with fractional order filters. The results from the comparative analysis of their frequency characteristics are given below.

Julia Sets and Their Control in a Three-Dimensional Discrete Fractional-Order Financial Model

2021 ◽  
Vol 31 (16) ◽  
Author(s):  
Zhongyuan Zhao ◽  
Yongping Zhang
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Julia Set ◽  
Julia Sets ◽  
Three Dimensional ◽  
Financial System ◽  
Order Theory ◽  
System Model ◽  
Financial Model ◽  
Fractal Characteristics

It is of great significance to study the three-dimensional financial system model based on the discrete fractional-order theory. In this paper, the Julia set of the three-dimensional discrete fractional-order financial model is identified to show its fractal characteristics. The sizes of the Julia sets need to be changed in some situations, so it is necessary to achieve control of the Julia sets. In combination with the characteristics of the model, two different controllers based on the fixed point are designed, and the control of the three-dimensional Julia sets is realized by adding the controllers into the model in different ways. Finally, the simulation graphs show that the controllers can effectively control the fractal behaviors.

The Filtering Mechanism Modeling and Simulation of Passive Power Filter Based on Differentiator Circuit

2012 ◽  
Vol 430-432 ◽  
pp. 1593-1596
Author(s):  
Wan Neng Yu ◽  
Su Wen Li ◽  
Min Ying Zheng
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Integer Order ◽  
Filter Performance ◽  
Power Filter ◽  
Fractional Order Differential Equations ◽  
Passive Power ◽  
The Mathematical Model

Traditional continuous-time filters are of integer order which the power loss of passive power filter is general very much. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations. In this work, firstly, the passive elements were described with fractional-order differential equations depending on the introduction of fractional calculus application research. Secondly, the mathematical model of fractional-order filters was derived and discussed which includes high impedance at a certain frequency and low impedance at others, and the integer-order filters are only a tight subset of fractional-order filters that are testified. At last, the filter design idea to the fractional-order domain is developed and the better filter performance of the fractional-order passive power filter is validated by the mathematical model analysis and simulation results.

scholarly journals Can Fractional Calculus be Generalized: Problems and Efforts

2018 ◽  
Vol 11 (4) ◽  
pp. 1058-1099
Author(s):  
Syamal K. Sen ◽  
J. Vasundhara Devi ◽  
R.V.G. Ravi Kumar
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Fractional Order Calculus ◽  
Integer Order ◽  
Classical Calculus ◽  
Pros And Cons

Fractional order calculus always includes integer-order too. The question that crops up is: Can it be a widely accepted generalized version of classical calculus? We attempt to highlight the current problems that come in the way to define the fractional calculus that will be universally accepted as a perfect generalized version of integer-order calculus and to point out the efforts in this direction. Also, we discuss the question: Given a non-integer fractional order differential equation as a mathematical model can we readily write the corresponding physical model and vice versa in the same way as we traditionally do for classical differential equations? We demonstrate numerically computationally the pros and cons while addressing the questions keeping in the background the generalization of the inverse of a matrix.

scholarly journals Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Sunil Kumar Mishra ◽  
Dinesh Chandra
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Tracking Control ◽  
Inverted Pendulum ◽  
Fitness Function ◽  
Pid Controllers ◽  
Simulink Model ◽  
System A ◽  
Simulation Results ◽  
Fractional Order Pid

This work focuses on the use of fractional calculus to design robust fractional-order PID (PIλDμ) controller for stabilization and tracking control of inverted pendulum (IP) system. A particle swarm optimisation (PSO) based direct tuning technique is used to design two PIλDμcontrollers for IP system without linearizing the actual nonlinear model. The fitness function is minimized by running the SIMULINK model of IP system according to the PSO program in MATLAB. The performance of proposed PIλDμcontrollers is compared with two PID controllers. Simulation results are also obtained by adding disturbances to the model to show the robustness of the proposed controllers.

scholarly journals Fractional calculus in image processing: a review

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Qi Yang ◽  
Dali Chen ◽  
Tiebiao Zhao ◽  
YangQuan Chen
Keyword(s):  
Image Processing ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Free Parameter ◽  
Science And Engineering ◽  
Fractional Systems ◽  
Integer Order

AbstractOver the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional systems. Due to the extra free parameter order

Sign in / Sign up

Export Citation Format

Share Document