**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5846

# Search results for: fractional order bounded variation

##### 5846 Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising

**Authors:**
Jianwei Ma,
Diriba Gemechu

**Abstract:**

**Keywords:**
Anisotropic total fractional order variation,
fractional
order bounded variation,
seismic random noise attenuation,
Split
Bregman Algorithm.

##### 5845 Quality Factor Variation with Transform Order in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
K. Pardha Saradhi,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Quality Factor,
Fractional Fourier span,
transient signals.

##### 5844 Stability of Interval Fractional-order Systems with Order 0 < α < 1

**Authors:**
Hong Li,
Shou-ming Zhong,
Hou-biao Li

**Abstract:**

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

**Keywords:**
Interval fractional-order systems,
linear matrix inequality (LMI),
asymptotical stability.

##### 5843 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Perturbation,
Fractional Fourier span,
amplitude,
phase,
transform order,
filterbanks.

##### 5842 Fractional Order Feedback Control of a Ball and Beam System

**Authors:**
Santosh Kr. Choudhary

**Abstract:**

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

**Keywords:**
Fractional order calculus,
fractional order controller,
fractional order system,
ball and beam system,
PIλDμ controller,
modelling,
simulation.

##### 5841 A Design of Fractional-Order PI Controller with Error Compensation

**Authors:**
Mazidah Tajjudin,
Norhashim Mohd Arshad,
Ramli Adnan

**Abstract:**

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

**Keywords:**
Fractional-order PI,
Ziegler-Nichols tuning,
Oustaloup's Recursive Approximation,
steam temperature control.

##### 5840 Realization of Fractional-Order Capacitors with Field-Effect Transistors

**Authors:**
Steve Hung-Lung Tu,
Yu-Hsuan Cheng

**Abstract:**

**Keywords:**
Fractional-order,
field-effect transistors,
RC
transmission lines.

##### 5839 Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI

**Authors:**
Elham Amini Boroujeni,
Hamid Reza Momeni

**Abstract:**

**Keywords:**
Fractional order calculus,
Fractional order observer,
Linear matrix inequality,
Nonlinear Systems,
Observer based
Controller.

##### 5838 Stability Analysis of Fractional Order Systems with Time Delay

**Authors:**
Hong Li,
Shou-Ming Zhong,
Hou-Biao Li

**Abstract:**

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

**Keywords:**
Fractional order systems,
Time delay,
Characteristic equation.

##### 5837 On Fractional (k,m)-Deleted Graphs with Constrains Conditions

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

**Keywords:**
Graph,
degree condition,
fractional k-factor,
fractional (k,
m)-deleted graph.

##### 5836 A Neighborhood Condition for Fractional k-deleted Graphs

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.

**Keywords:**
Graph,
minimum degree,
neighborhood union,
fractional k-factor,
fractional k-deleted graph.

##### 5835 Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay

**Authors:**
Liqiong Liu,
Shouming Zhong

**Abstract:**

In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.

**Keywords:**
Finite-time stabilization,
fractional-order system,
Gronwall inequality.

##### 5834 Measurement Fractional Order Sallen-Key Filters

**Authors:**
Ahmed Soltan,
Ahmed G. Radwan,
Ahmed M. Soliman

**Abstract:**

This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

**Keywords:**
Analog Filter,
Low-Pass Filter,
Fractance,
Sallen-Key,
Stability.

##### 5833 Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing

**Authors:**
Changhong Guo,
Shaomei Fang,
Yong He

**Abstract:**

**Keywords:**
European option pricing,
fractional Black-Scholes
equations,
fractional G-Brownian motion,
Taylor’s series of fractional
order,
uncertain volatility.

##### 5832 Application of Fractional Model Predictive Control to Thermal System

**Authors:**
Aymen Rhouma,
Khaled Hcheichi,
Sami Hafsi

**Abstract:**

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller*.*

**Keywords:**
Fractional model predictive control,
fractional order systems,
thermal system.

##### 5831 Synthesis of Digital Circuits with Genetic Algorithms: A Fractional-Order Approach

**Authors:**
Cecília Reis,
J. A. Tenreiro Machado,
J. Boaventura Cunha

**Abstract:**

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

**Keywords:**
Circuit design,
fractional-order systems,
genetic algorithms,
logic circuits.

##### 5830 Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems

**Authors:**
Kazem Ghanbari,
Yousef Gholami

**Abstract:**

**Keywords:**
Fractional derivatives and integrals,
Hamiltonian
system,
Lyapunov type inequalities,
stability,
disconjugacy.

##### 5829 Synthesis of Logic Circuits Using Fractional-Order Dynamic Fitness Functions

**Authors:**
Cecília Reis,
J. A. Tenreiro Machado,
J. Boaventura Cunha

**Abstract:**

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

**Keywords:**
Circuit design,
fractional-order systems,
genetic algorithms,
logic circuits

##### 5828 Backstepping Design and Fractional Derivative Equation of Chaotic System

**Authors:**
Ayub Khan,
Net Ram Garg,
Geeta Jain

**Abstract:**

In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

**Keywords:**
Backstepping method,
Fractional order,
Synchronization.

##### 5827 Confidence Intervals for the Coefficients of Variation with Bounded Parameters

**Authors:**
Jeerapa Sappakitkamjorn,
Sa-aat Niwitpong

**Abstract:**

In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.

**Keywords:**
Bounded parameters,
coefficient of variation,
confidence interval,
Monte Carlo simulation.

##### 5826 A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations

**Authors:**
Sachin Bhalekar

**Abstract:**

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.

**Keywords:**
Caputo derivative,
delay,
stability,
chaos.

##### 5825 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon

**Authors:**
Haniye Dehestani,
Yadollah Ordokhani

**Abstract:**

**Keywords:**
Collocation method,
fractional partial differential
equations,
Legendre-Laguerre functions,
pseudo-operational matrix
of integration.

##### 5824 Notes on Fractional k-Covered Graphs

**Authors:**
Sizhong Zhou,
Yang Xu

**Abstract:**

**Keywords:**
graph,
binding number,
fractional k-factor,
fractional k-covered graph.

##### 5823 Rate of Convergence for Generalized Baskakov-Durrmeyer Operators

**Authors:**
Durvesh Kumar Verma,
P. N. Agrawal

**Abstract:**

In the present paper, we consider the generalized form of Baskakov Durrmeyer operators to study the rate of convergence, in simultaneous approximation for functions having derivatives of bounded variation.

**Keywords:**
Bounded variation,
Baskakov-Durrmeyer operators,
simultaneous approximation,
rate of convergence.

##### 5822 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

**Authors:**
Changjin Xu,
Peiluan Li

**Abstract:**

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 to show the effectiveness of the approach presented in this paper.

**Keywords:**
Fractional predator-prey model,
laplace transform,
characteristic equation.

##### 5821 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems

**Authors:**
Ali Dorostkar

**Abstract:**

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

**Keywords:**
Tangent line,
fractional dimension,
root,
optimization problem.

##### 5820 Fractional-Order PI Controller Tuning Rules for Cascade Control System

**Authors:**
Truong Nguyen Luan Vu,
Le Hieu Giang,
Le Linh

**Abstract:**

The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

**Keywords:**
Fractional calculus,
fractional–order proportional integral controller,
cascade control system,
internal model control approach.

##### 5819 An Efficient Algorithm for Delay Delay-variation Bounded Least Cost Multicast Routing

**Authors:**
Manas Ranjan Kabat,
Manoj Kumar Patel,
Chita Ranjan Tripathy

**Abstract:**

**Keywords:**
EDVBM,
Heuristic algorithm,
Multicast tree,
QoS
routing,
Shortest path.

##### 5818 Robust Fractional-Order PI Controller with Ziegler-Nichols Rules

**Authors:**
Mazidah Tajjudin,
Mohd Hezri Fazalul Rahiman,
Norhashim Mohd Arshad,
Ramli Adnan

**Abstract:**

In process control applications, above 90% of the controllers are of PID type. This paper proposed a robust PI controller with fractional-order integrator. The PI parameters were obtained using classical Ziegler-Nichols rules but enhanced with the application of error filter cascaded to the fractional-order PI. The controller was applied on steam temperature process that was described by FOPDT transfer function. The process can be classified as lag dominating process with very small relative dead-time. The proposed control scheme was compared with other PI controller tuned using Ziegler-Nichols and AMIGO rules. Other PI controller with fractional-order integrator known as F-MIGO was also considered. All the controllers were subjected to set point change and load disturbance tests. The performance was measured using Integral of Squared Error (ISE) and Integral of Control Signal (ICO). The proposed controller produced best performance for all the tests with the least ISE index.

**Keywords:**
PID controller,
fractional-order PID controller,
PI
control tuning,
steam temperature control,
Ziegler-Nichols tuning.

##### 5817 Frequency-Domain Design of Fractional-Order FIR Differentiators

**Authors:**
Wei-Der Chang,
Dai-Ming Chang,
Eri-Wei Chiang,
Chia-Hung Lin,
Jian-Liung Chen

**Abstract:**

**Keywords:**
Fractional-order differentiator,
FIR digital filter,
Differential evolution algorithm.