Contraction Analysis by Integer Order and Fractional Order Infinitesimal Variations

2014 ◽  
pp. 181-197 ◽  
Author(s):  
Bijnan Bandyopadhyay ◽  
Shyam Kamal
Keyword(s):  
Fractional Order ◽  
Integer Order

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

The multi-model approach for fractional-order systems modelling

2016 ◽  
Vol 40 (1) ◽  
pp. 331-340 ◽  
Author(s):  
Samia Talmoudi ◽  
Moufida Lahmari
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Global Model ◽  
Fractional Order Systems ◽  
New Approach ◽  
Physical Systems ◽  
Integer Order ◽  
Systems Modelling ◽  
Model Approach

Currently, fractional-order systems are attracting the attention of many researchers because they present a better representation of many physical systems in several areas, compared with integer-order models. This article contains two main contributions. In the first one, we suggest a new approach to fractional-order systems modelling. This model is represented by an explicit transfer function based on the multi-model approach. In the second contribution, a new method of computation of the validity of library models, according to the frequency [Formula: see text], is exposed. Finally, a global model is obtained by fusion of library models weighted by their respective validities. Illustrative examples are presented to show the advantages and the quality of the proposed strategy.

OPCL Coupling of Mixed Integer-Fractional Order oscillators: Tree and Chain Implementation

2021 ◽  
Author(s):  
Adedayo Oke Adelakun
Keyword(s):  
Fractional Order ◽  
Mixed Integer ◽  
Complete Synchronization ◽  
Amplitude Death ◽  
Integer Order ◽  
Simulation Results ◽  
Coupled Circuits ◽  
Tree Type ◽  
Chain Type

Abstract OPCL Coupling of Integer-order and fractional-order Sprott-A systems using off-shelf components are constructed. Fractance configurations such as chain-type and tree-type were designed using a fractional-order capacitor and fractional-order resistor, respectively. The simulation results of the coupled circuits reveal the transition between complete synchronization (CS) to Anti-synchronization (AS) and vice versa via Amplitude death (AD).

Finite deformation and fractional order viscoelasticity of an auxetic foam

2022 ◽  
pp. 1045389X2110643
Author(s):  
Eugenia Stanisauskis ◽  
Paul Miles ◽  
William Oates
Keyword(s):  
Fractional Order ◽  
Finite Deformation ◽  
Viscoelastic Behavior ◽  
Integer Order ◽  
Relaxation Effects ◽  
Viscoelastic Parameters ◽  
Rate Dependent ◽  
Improve Model ◽  
Model Predictions ◽  
And Performance

Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

Angular control of differential shape-memory alloy spring actuator for underactuated dynamic system

2021 ◽  
pp. 107754632110216
Author(s):  
M Banu Sundareswari ◽  
G Then Mozhi ◽  
K Dhanalakshmi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Control Effort ◽  
Control Laws ◽  
Integer Order ◽  
Two Degree Of Freedom ◽  
Outer Primary

This article dwells on two technical aspects, the design and implementation of an upgraded version of the differential shape-memory alloy–based revolute actuator/rotary actuating mechanism for stabilization and position control of a two-degree-of-freedom centrally hinged ball on beam system. The actuator is configured with differential and inclined placement of shape-memory alloy springs to provide bidirectional angular shift. The shape-memory alloy spring actuator occupies a smaller space and provides more extensive reformation with justifiable actuation force than an equally able shape-memory alloy wire. The cross or diagonal architecture of shape-memory alloy springs provides force amplification and reduces the actuator’s control effort. The shape-memory alloy spring–embodied actuator’s function is exemplified by the highly dynamic underactuated custom-designed ball balancing system. The ball position control is experimentally demonstrated by cascade control using the control laws that have been unattempted for shape-memory alloy actuated systems; the ball is positioned with linear (integer-order and fractional-order) proportional–integral–derivative controllers optimized with genetic algorithm and particle swarm optimization at the outer/primary loop. Angular control of the shape-memory alloy actuated beam is obtained with nonlinear (integer-order and fractional-order sliding mode control) control algorithms in the inner/secondary loop.

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