scholarly journals Stability Analysis Of Delayed Fractional Integro-Differential Equations With Applications Of RLC Circuits

2020 ◽  
Vol 26 (1) ◽  
pp. 74-100
Author(s):  
Mohamed El-Borhamy ◽  
Alaa Ahmed
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Critical Frequency ◽  
Approximation Techniques ◽  
Characteristic Exponents ◽  
Rlc Circuit ◽  
The Stability ◽  
Rlc Circuits ◽  
The Impact

 This article presents the stability analysis of delay integro-differentialequations with fractional order derivative via some approximation techniques forthe derived nonlinear terms of characteristic exponents. Based on these techniques,the existence of some analytical solutions at the neighborhood of their equilibriumpoints is proved. Stability charts are constructed and so both of the critical timedelay and critical frequency formulae are obtained. The impact of this work into thegeneral RLC circuit applications exposing the delay and fractional order derivativesis discussed.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

Fractional-order COVID-19 pandemic outbreak: Modeling and stability analysis

2021 ◽  
Author(s):  
Iqbal M. Batiha ◽  
Shaher Momani ◽  
Adel Ouannas ◽  
Zaid Momani ◽  
Samir B. Hadid
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Differential Operators ◽  
Euler Method ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Established Disease ◽  
Acute Infectious Disease ◽  
The Stability ◽  
The Impact

Today, the entire world is witnessing an enormous upsurge in coronavirus pandemic (COVID-19 pandemic). Confronting such acute infectious disease, which has taken multiple victims around the world, requires all specialists in all fields to devote their efforts to seek effective treatment or even control its disseminate. In the light of this aspect, this work proposes two new fractional-order versions for one of the recently extended forms of the SEIR model. These two versions, which are established in view of two fractional-order differential operators, namely, the Caputo and the Caputo–Fabrizio operators, are numerically solved based on the Generalized Euler Method (GEM) that considers Caputo sense, and the Adams–Bashforth Method (ABM) that considers Caputo–Fabrizio sense. Several numerical results reveal the impact of the fractional-order values on the two established disease models, and the continuation of the COVID-19 pandemic outbreak to this moment. In the meantime, some novel results related to the stability analysis and the basic reproductive number are addressed for the proposed fractional-order Caputo COVID-19 model. For declining the total of individuals infected by such pandemic, a new compartment is added to the proposed model, namely the disease prevention compartment that includes the use of face masks, gloves and sterilizers. In view of such modification, it is turned out that the performed addition to the fractional-order Caputo COVID-19 model yields a significant improvement in reducing the risk of COVID-19 spreading.

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

A Survey of Fractional-Order Neural Networks

2017 ◽  
Author(s):  
Shuo Zhang ◽  
YangQuan Chen ◽  
Yongguang Yu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Computational Science ◽  
General Introduction ◽  
Analysis Methods ◽  
Recent Trends ◽  
The Stability

In this paper, the literature of fractional-order neural networks is categorized and discussed, which includes a general introduction and overview of fractional-order neural networks. Various application areas of fractional-order neural networks have been found or used, and will be surveyed and summarized such as neuroscience, computational science, control and optimization. Recent trends in dynamics of fractional-order neural networks are presented and discussed. The results, especially the stability analysis of fractional-order neural networks, are reviewed and different analysis methods are compared. Furthermore, the challenges and conclusions of fractional-order neural networks are given.

GUI Toolbox for Approximation of Fractional Order Parameters With Application to Control of pH Neutralization Process

2019 ◽  
pp. 260-286
Author(s):  
Bingi Kishore ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassan ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Order Parameters ◽  
Fractional Order Systems ◽  
Approximation Techniques ◽  
Numerical Tools ◽  
Neutralization Process ◽  
Fractional Order Pid ◽  
Ph Neutralization ◽  
Ph Neutralization Process

Fractional-order systems have been applied in many engineering applications. A key issue with the application of such systems is the approximation of fractional-order parameters. The numerical tools for the approximation of fractional-order parameters gained attention recently. However, available toolboxes in the literature do not have a direct option to approximate higher order systems and need improvements with the graphical, numerical, and stability analysis. Therefore, this chapter proposes a MATLAB-based GUI for the approximation of fractional-order operators. The toolbox is made up of four widely used approximation techniques, namely, Oustaloup, refined Oustaloup, Matsuda, and curve fitting. The toolbox also allows numerical and stability analysis for evaluating the performance of approximated transfer function. To demonstrate the effectiveness of the developed GUI, a simulation study is conducted on fractional-order PID control of pH neutralization process. The results show that the toolbox can be effectively used to approximate and analyze the fractional-order systems.

scholarly journals Impedance Aggregation Method of Multiple Wind Turbines and Accuracy Analysis

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2035 ◽  
Author(s):  
Liang Chen ◽  
Heng Nian ◽  
Yunyang Xu
Keyword(s):  
Stability Analysis ◽  
Reference Frame ◽  
Wind Turbines ◽  
Power Distribution ◽  
Wind Farm ◽  
System Level ◽  
Small Signal ◽  
Impedance Model ◽  
The Stability ◽  
The Impact

The sequence domain impedance modeling of wind turbines (WTs) has been widely used in the stability analysis between WTs and weak grids with high line impedance. An aggregated impedance model of the wind farm is required in the system-level analysis. However, directly aggregating WT small-signal impedance models will lead to an inaccurate aggregated impedance model due to the mismatch of reference frame definitions among different WT subsystems, which may lead to inaccuracy in the stability analysis. In this paper, we analyze the impacts of the reference frame mismatch between a local small-signal impedance model and a global one on the accuracy of aggregated impedance and the accuracy of impedance-based stability analysis. The results revealed that the impact is related to the power distribution of the studied network. It was found that that the influence of mismatch on stability analysis became subtle when subsystems were balanced loaded. Considering that balanced loading is a common configuration of the practical application, direct impedance aggregation by local small-signal models can be applied due to its acceptable accuracy.

Uncertainty Model of Concrete Elastic Modulus Effect to Critical Reinforced Concrete Buckling Load

2014 ◽  
Vol 931-932 ◽  
pp. 525-528
Author(s):  
Sanguan Vongchavalitkul
Keyword(s):  
Elastic Modulus ◽  
Stability Analysis ◽  
Statistical Data ◽  
Stability Index ◽  
Buckling Load ◽  
Design Code ◽  
Critical Buckling Load ◽  
Uncertainty Model ◽  
The Stability ◽  
The Impact

There are differences in each countrys design code for concrete elastic modulus that cause uncertainty in stability analysis of critical buckling load column. This paper investigates the impact of uncertainty on concrete elastic modulus for designing of critical buckling load of building column. The statistical data on materials and applied load being collected in Thailand are used together with an investigation on the uncertainty of the concrete elastic modulus in the design code from 8 countries. Finally the Monte Carlo simulation is used to find out the stability index in term of reliability index. The results show that the uncertainty of the concrete elastic modulus plays an important role in stability analysis and should be considered in the design.

Stability Analysis about the Impact of Soft Rock to the Underground Cavern Group

2013 ◽  
Vol 706-708 ◽  
pp. 560-564
Author(s):  
Yi Huan Zhu ◽  
Guo Jian Shao ◽  
Zhi Gao Dong
Keyword(s):  
Finite Element ◽  
Rock Mass ◽  
Stability Analysis ◽  
Soft Rock ◽  
Element Model ◽  
Underground Excavation ◽  
Power Station ◽  
Excavation Process ◽  
The Stability ◽  
The Impact

Soft rock is frequently encountered in underground excavation process. It is difficult to excavate and support in soft rock mass which has low strength, large deformation and needs much time to be out of shape but little time to be self-stabilized. Based on a large underground power station, finite element model analysis was carried out to simulate the excavation process and the results of displacement, stress and plasticity area were compared between supported and unsupported conditions to evaluate the stability of the rock mass.

On the Stability of the Impact Damper

1966 ◽  
Vol 33 (3) ◽  
pp. 586-592 ◽  
Author(s):  
S. F. Masri ◽  
T. K. Caughey
Keyword(s):  
Exact Solution ◽  
Stability Analysis ◽  
Asymptotically Stable ◽  
Impact Damper ◽  
The Stability ◽  
The Impact

The exact solution for the symmetric two-impacts-per-cycle motion of the impact damper is derived analytically, and its asymptotically stable regions are determined. The stability analysis defines the zones where the modulus of all the eigenvalues of a certain matrix relating conditions after each of two consecutive impacts is less than unity.

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