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fractional order Environmental and Economic Model Investigations Using Artificial Neural Network

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Computers, Materials & Continua 2023年第1期74卷 1735-1748页

作者： Wajaree Weera Chantapish Zamart Zulqurnain Sabir Muhammad Asif Zahoor Raja Afaf S.Alwabli S.R.Mahmoud Supreecha Wongaree Thongchai Botmart Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematical Sciences UAE UniversityP.O.Box 15551Al AinUAE Future Technology Research Center National Yunlin University of Science and Technology123 University RoadSection 3DouliouYunlin64002Taiwan Department of Biological Sciences Rabigh College of Science and ArtsKing Abdulaziz UniversityRabighSaudi Arabia GRC Department Faculty of Applied StudiesJeddahKing Abdulaziz UniversityRabighSaudi Arabia Institute of General Education Udon Thani Rajabhat UniversityUdon Thani41000Thailand

The motive of these investigations is to provide the importance and significance of the fractional order(FO)derivatives in the nonlinear environmental and economic(NEE)model,i.e.,FO-NEE *** dynamics of the NEE model achieves more precise by using the form of the FO *** investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this *** composition of the FO-NEEmodel is classified into three classes,execution cost of control,system competence of industrial elements and a new diagnostics technical exclusion *** mathematical FO-NEE system is numerically studied by using the artificial neural networks(ANNs)along with the Levenberg-Marquardt backpropagation method(ANNs-LMBM).Three different cases using the FO derivative have been examined to present the numerical performances of the FO-NEE *** data is selected to solve the mathematical FO-NEE system is executed as 70%for training and 15%for both testing and *** exactness of the proposed ANNs-LMBM is observed through the comparison of the obtained and the Adams-Bashforth-Moulton database *** ratify the aptitude,validity,constancy,exactness,and competence of the ANNs-LMBM,the numerical replications using the state transitions,regression,correlation,error histograms and mean square error are also described.

关键词： Environmental and economic model artificial neural networks fractional order nonlinear Levenberg-Marquardt backpropagation

Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization

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Chinese Physics B 2010年第12期19卷 97-104页

作者：牛玉军王兴元年福忠王明军 School of Electronic & Information Engineering Dalian University of Technology

Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.

关键词： dynamic analysis fractional order generalized projective synchronization Laplace transformation

Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system

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Chinese Physics B 2018年第12期27卷 538-545页

作者： Xiang Gao Diyi Chen Hao Zhang Beibei Xu Xiangyu Wang Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas Ministry of EducationNorthwest A & F University Institute of Water Resources and Hydropower Research Northwest A & F University Australasian Joint Research Centre for Building Information Modelling School of Built Environment Curtin University

Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.

关键词： fast–slow dynamics fractional order nonlinear dynamics hydropower generation system

A Stochastic Study of the fractional order Model of Waste Plastic in Oceans

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Computers, Materials & Continua 2022年第11期73卷 4441-4454页

作者： Muneerah Al Nuwairan Zulqurnain Sabir Muhammad Asif Zahoor Raja Maryam Alnami Hanan Almuslem Department of Mathematics and Statistics College of ScienceKing Faisal UniversityP.O.Box 400Al-Ahsa31982Saudi Arabia Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan

In this paper,a fractional order model based on the management of waste plastic in the ocean(FO-MWPO)is numerically *** mathematical form of the FO-MWPO model is categorized into three components,waste plastic,Marine debris,and *** stochastic numerical solvers using the Levenberg-Marquardt backpropagation neural networks(LMQBP-NNs)have been applied to present the numerical solutions of the FO-MWPO *** competency of the method is tested by taking three variants of the FO-MWPO model based on the fractional order *** data ratio is provided for training,testing and authorization is 77%,12%,and 11%*** exactness of LMQBP-NNs is observed by using the comparative performances of the obtained and the Adams-BashforthMoulton *** verify the competence,validity,capability,exactness,and consistency of LMQBP-NNs,the performances have been obtained using the regression,state transitions,error histograms,correlation and mean square error.

关键词： fractional order ocean Adams-Bashforth-Moulton LevenbergMarquardt backpropagation numerical solutions

Projective synchronization of a complex network with different fractional order chaos nodes

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Chinese Physics B 2011年第1期20卷 224-228页

作者：王明军王兴元牛玉军 School of Electronic and Information Engineering Dalian University of Technology School of Information Engineering Dalian University

Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.

关键词： fractional order different-structure complex network projective synchronization

The feedback control of fractional order unified chaotic system

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Chinese Physics B 2010年第2期19卷 145-148页

作者：齐冬莲杨捷张建良 College of Electrical Engineering Zhejiang University

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

关键词： state feedback control fractional order unified chaotic system Lyapunov function

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED fractional order NEURAL NETWORKS

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Acta Mathematica Scientia 2022年第4期42卷 1273-1292页

作者： Anbalagan PRATAP Ramachandran RAJA Jinde CAO Chuangxia HUANG Jehad ALZABUT Ovidiu BAGDASAR Department of Mathematics Alagappa UniversityKaraikudi 630004India Ramanujan Centre for Higher Mathematics Alagappa UniversityKaraikudi 630004India School of Mathematics Southeast UniversityNanjing 211189China Yonsei Frontier Lab Yonsei UniversitySeoul03722South Korea Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha410114China Department of Mathematics and General Sciences Prince Sultan UniversityRiyadh 12435Saudi Arabia Department of Electronics Computing and MathematicsUniversity of DerbyUnited Kingdom

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical *** designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control ***,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

关键词： O(t^(-β))-synchronization asymptotic synchronization BAM neural networks fractional order state feedback control law

A fractional order Fast Repetitive Control Paradigm of Vienna Rectifier for Power Quality Improvement

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Computer Modeling in Engineering & Sciences 2023年第2期134卷 1159-1176页

作者： Sue Wang Xintao Luo Saleem Riaz Haider Zaman Chaohong Zhou Pengfei Hao School of Electrical and Control Engineering Shaanxi University of Science and TechnologyXi’anChina School of Automation Northwestern Polytechnical UniversityXi’anChina Electronics Engineering Department University of Engineering and Technology PeshawarKhyberPakhtunKhwaPakistan

Due to attractive features,including high efficiency,low device stress,and ability to boost voltage,a Vienna rectifier is commonly employed as a battery charger in an electric vehicle(EV).However,the 6k±1 harmonics in the acside current of the Vienna rectifier deteriorate theTHDof the ac current,thus lowering the power ***,the current closed-loop for suppressing 6k±1 harmonics is essential tomeet the desired total harmonic distortion(THD).Fast repetitive control(FRC)is generally adopted;however,the deviation of power grid frequency causes delay link in the six frequency fast repetitive control to become non-integer and the tracking performance to *** paper presents the detailed parameter design and calculation of fractional order fast repetitive controller(FOFRC)for the non-integer delay *** finite polynomial approximates the non-integer delay link through the Lagrange interpolation *** comparing the frequency characteristics of traditional repetitive control,the effectiveness of the FOFRC strategy is ***,simulation and experiment validate the steadystate performance and harmonics suppression ability of FOFRC.

关键词： Vienna rectifier fast repetitive control fractional order performance analysis

An Artificial Approach for the fractional order Rape and Its Control Model

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Computers, Materials & Continua 2023年第2期74卷 3421-3438页

作者： Wajaree Weera Zulqurnain Sabir Muhammad Asif Zahoor Raja Salem Ben Said Maria Emilia Camargo Chantapish Zamart Thongchai Botmart Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Mathematics Near East UniversityNicosia99138Cyprus Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan Department of Mathematical Science College of ScienceUnited Arab Emirates UniversityAl AinAbu Dhabi15551UAE Graduate Program in Administration Federal University of Santa MariaSanta Maria93458Brazil

The current investigations provide the solutions of the nonlinear fractional order mathematical rape and its controlmodel using the strength of artificial neural networks(ANNs)along with the Levenberg-Marquardt backpropagation approach(LMBA),i.e.,artificial neural networks-Levenberg-Marquardt backpropagation approach(ANNs-LMBA).The fractional order investigations have been presented to find more realistic results of the mathematical form of the rape and its control *** differential mathematical form of the nonlinear fractional order mathematical rape and its control model has six classes:susceptible native girls,infected immature girls,susceptible knowledgeable girls,infected knowledgeable girls,susceptible rapist population and infective rapist *** rape and its control differential system using three different fractional order values is authenticated to perform the correctness of *** data is used to present the rape and its control differential system is designated as 70%for training,14%for authorization and 16%for *** obtained performances of the ANNs-LMBA are compared with the dataset of the Adams-Bashforth-Moulton *** substantiate the consistency,aptitude,validity,exactness,and capability of the LMBA neural networks,the obtained numerical values are provided using the state transitions(STs),correlation,regression,mean square error(MSE)and error histograms(EHs).

关键词： Rape and its control differential system neural networks fractional order levenberg-marquardt backpropagation approach reference solutions