An innovative fixed-pole numerical approximation for fractional order systems

2016 ◽  
Vol 62 ◽  
pp. 94-102 ◽  
Author(s):  
Yiheng Wei ◽  
Peter W. Tse ◽  
Bin Du ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Numerical Approximation ◽  
Fractional Order Systems ◽  
Fixed Pole

Fixed pole based modeling and simulation schemes for fractional order systems

2019 ◽  
Vol 84 ◽  
pp. 43-54 ◽  
Author(s):  
Yiheng Wei ◽  
Jiachang Wang ◽  
Tianyu Liu ◽  
Yong Wang
Keyword(s):  
Modeling And Simulation ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Fixed Pole

Multiple Fixed Pole-Based Rational Approximation for Fractional Order Systems

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Yiheng Wei ◽  
Hui Zhang ◽  
Yuqing Hou ◽  
Kun Cheng
Keyword(s):  
Fractional Order ◽  
Rational Approximation ◽  
Relative Degree ◽  
Initial Instant ◽  
Fractional Order Systems ◽  
Fractional Operators ◽  
Initial State ◽  
Fixed Pole ◽  
Pole Scheme

Abstract Our topic is the rational approximation of fractional order systems under Riemann–Liouville definition. This is a venerable, vast, fundamental area which attracts ongoing attention in coming years. In this work, the multiple fixed-pole scheme is developed. First, new schemes with different relative degree are developed to approximate fractional operators. Then, the fractional order is extended to the case of α>1. A discussion is made on the uniformity between the differentiator-based method and the integrator-based method. Afterward, the multiplicity of pole/zero is further generalized. In this framework, the nonzero initial instant and nonzero initial state are considered. Four examples are finally provided to show the feasibility and effectiveness of the developed algorithms.

State-space analysis of linear fractional-order systems

2008 ◽  
Vol 42 (6-8) ◽  
pp. 825-838 ◽  
Author(s):  
Saïd Guermah ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Space Analysis ◽  
State Space Analysis

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

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