Modeling and analysis of double fractional order Jeffreys viscoelastic fluids flow

2022 ◽  
Vol 124 ◽  
pp. 107630
Author(s):  
Shengna Liu ◽  
Weidong Yang ◽  
Liancun Zheng
Keyword(s):  
Fractional Order ◽  
Viscoelastic Fluids ◽  
Modeling And Analysis

Modeling and analysis of a fractional-order prey-predator system incorporating harvesting

2020 ◽  
Author(s):  
Manotosh Mandal ◽  
Soovoojeet Jana ◽  
Swapan Kumar Nandi ◽  
T. K. Kar
Keyword(s):  
Fractional Order ◽  
Modeling And Analysis ◽  
Predator System

scholarly journals Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 511 ◽  
Author(s):  
Ivo Petráš ◽  
Ján Terpák
Keyword(s):  
Time Series ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Long Memory ◽  
Real Data ◽  
Data Set ◽  
Modeling And Analysis ◽  
Long Memory Process ◽  
Real Process ◽  
Definition Of

This paper deals with the application of the fractional calculus as a tool for mathematical modeling and analysis of real processes, so called fractional-order processes. It is well-known that most real industrial processes are fractional-order ones. The main purpose of the article is to demonstrate a simple and effective method for the treatment of the output of fractional processes in the form of time series. The proposed method is based on fractional-order differentiation/integration using the Grünwald–Letnikov definition of the fractional-order operators. With this simple approach, we observe important properties in the time series and make decisions in real process control. Finally, an illustrative example for a real data set from a steelmaking process is presented.

Modeling and analysis of a single-phase fractional-order voltage source pulse width modulation rectifier

2020 ◽  
Vol 479 ◽  
pp. 228821
Author(s):  
Junhua Xu ◽  
Xiaocong Li ◽  
Xuanren Meng ◽  
Jianbo Qin ◽  
Hui Liu
Keyword(s):  
Fractional Order ◽  
Pulse Width ◽  
Single Phase ◽  
Pulse Width Modulation ◽  
Voltage Source ◽  
Modeling And Analysis

Fractional Order Modeling and Analysis of Buck-Boost Converter

2015 ◽  
Vol 789-790 ◽  
pp. 842-848
Author(s):  
Li Feng Yi ◽  
Kai Ru Zhang ◽  
Jun Liu
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Fractional Calculus ◽  
Simulation Model ◽  
Fractional Order ◽  
Theoretical Foundation ◽  
Boost Converter ◽  
Modeling And Analysis ◽  
Simulation Results ◽  
Conduction Mode

Considered the theoretical foundation of fractional order, the fractional mathematical model of the Buck-Boost converter in continuous conduction mode operation is built and analyzed in theory. Based on the improved Oustaloup fractional calculus for filter algorithm, the simulation model is framed by using the Matlab/Simulink software. And the simulation results are compared with that of integer order. It proves the correctness of the fractional order mathematical model and the theoretical analysis.

scholarly journals Fractional-Order Modeling and Analysis of a Variable Structure Hybrid Energy Storage System for EVs

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jianlin Wang ◽  
Dan Xu ◽  
Jiahui Zhou ◽  
Jinlu Mao
Keyword(s):  
Energy Storage ◽  
Nonlinear Control ◽  
Fractional Order ◽  
Electric Vehicles ◽  
Storage System ◽  
Energy Storage System ◽  
Modeling And Analysis ◽  
Hybrid Energy ◽  
Hybrid Energy Storage ◽  
Hybrid Energy Storage System

Hybrid energy storage system has been widely studied as an important technology for electric vehicles. Since the hybrid energy storage system is a nonlinear and complex system, the modeling of the system and the high-precision nonlinear control strategy are technical difficulties for research. The establishment of a high-precision mathematical model of the hybrid energy storage system is the basis for the study of high-quality nonlinear control algorithms. Fortunately, the theory of fractional calculus can help build accurate mathematical models of hybrid energy storage systems. In order to obtain the high-quality nonlinear control strategy of this complex system, this paper, respectively, carried out fractional-order modeling and analysis on the three basic equivalent working states of the hybrid energy storage system of electric vehicles. Among them, the fractional-order average state space model is carried out for the equivalent Buck and Boost mode. Also, the steady-state analysis of the equivalent Dual-Boost mode is carried out by combining the fractional-order calculus theory with the equivalent small parameter variable method. Finally, the effectiveness and precision of the fractional-order model are proved by simulation and experiment.

On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models

2017 ◽  
Vol 18 (5) ◽  
pp. 315-325 ◽  
Author(s):  
Ivanka M. Stamova ◽  
Gani Tr. Stamov
Keyword(s):  
Fractional Calculus ◽  
Dynamic Behavior ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Mathematical Finance ◽  
Financial Systems ◽  
Modeling And Analysis ◽  
Modeling Approach ◽  
Suitable Tool ◽  
Impulsive Perturbations

AbstractIn this article, we introduce fractional-order Solow-type models as a new tool for modeling and analysis in mathematical finance. Sufficient conditions for the Mittag–Leffler stability of their states are derived. The main advantages of the proposed approach are using of fractional-order derivatives, whose nonlocal property makes the fractional calculus a suitable tool for modeling actual financial systems as well as using of impulsive perturbations which give an opportunity to control the dynamic behavior of the model. The modeling approach proposed in this article can be applied to investigate macroeconomic systems.

scholarly journals An impulsive delay discrete stochastic neural network fractional-order model and applications in finance

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6339-6352
Author(s):  
Martin Bohner ◽  
Ivanka Stamova
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Financial Assets ◽  
Order Model ◽  
Stochastic Neural Network ◽  
Modeling And Analysis ◽  
Fractional Order Model ◽  
Noise Disturbances ◽  
Impulsive Delay ◽  
Stochastic Term

In this paper, we propose a new tool for modeling and analysis in finance, introducing an impulsive discrete stochastic neural network (NN) fractional-order model. The main advantages of the proposed approach are: (i) Using NNs which can be trained without the restriction of a model to derive parameters and discover relationships, driven and shaped solely by the nature of the data; (ii) using fractional-order differences, whose nonlocal property makes the fractional calculus a suitable tool for modeling actual financial systems; (iii) using impulsive perturbations, which give an opportunity to control the dynamic behavior of the model; (iv) including a stochastic term, which allows to study the effect of noise disturbances generally existing in financial assets; (v) taking into account the existence of time delayed influences. The modeling approach proposed in this paper can be applied to investigate macroeconomic systems.

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