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Novel Computing for the Delay Differential Two-Prey and One-Predator System

Computers, Materials & Continua 2022年第10期73卷 249-263页

作者： Prem Junsawang Zulqurnain Sabir Muhammad Asif Zahoor Raja Soheil Salahshour Thongchai Botmart Wajaree Weera Department of Statistics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Future Technology Research Center National Yunlin University of Science and TechnologyDouliou64002Taiwan Faculty of Engineering and Natural Sciences Bahcesehir UniversityIstanbulTurkey Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator *** delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator ***,a stochastic numerical paradigm based artificial neural network(ANN)along with the levenberg-marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator *** different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the *** statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for *** exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−*** check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided.

关键词： Delay differential model dynamical system prey-predator levenberg-marquardt backpropagation MSE neural networks

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Dynamics of Fractional Differential Model for Schistosomiasis Disease

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Computers, Materials & Continua 2022年第10期73卷 981-999页

作者： Thongchai Botmart Wajaree Weera Muhammad Asif Zahoor Raja Zulqurnain Sabir Qusain Hiader Gilder Cieza Altamirano Plinio Junior Muro Solano Alfonso Tesen Arroyo Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Department of Mathematics University of GujratGujrat50700Pakistan Universidad Nacional Autónoma de Chota Chota06121Peru Universidad Nacional Pedro Ruiz Gallo Lambayeque14013Peru

In the present study,a design of a fractional order mathematical model is presented based on the schistosomiasis *** observe more accurate performances of the results,the use of fractional order derivatives in the mathematical model is introduce based on the schistosomiasis disease is *** preliminary design of the fractional order mathematical model focused on schistosomiasis disease is classified as follows:uninfected with schistosomiasis,infected with schistosomiasis,recovered from infection,susceptible snail unafflicted with schistosomiasis disease and susceptible snail afflicted with this *** solutions to the proposed system of the fractional order mathematical model will be presented using stochastic artificial neural network(ANN)techniques in conjunction with the levenbergmarquardt backpropagation(LMBP),referred to as *** illustrate the preciseness of the ANN-LMBP method,mathematical presentations of three different values focused on fractional order will be *** statics performances are taken in these investigations are 78%and 11%for both learning and *** accuracy of the ANN-LMBP method is determined by comparing the values obtained by the database Adams-Bash forth-Moulton *** simulation-based error histograms(EHs),MSE,recurrence,and state transitions(STs)will be offered to achieve the capability,accuracy,steadiness,abilities,and finesse of the ANN-LMBP method.

关键词： Biological model fractional order schistosomiasis disease artificial neural networks reference results levenberg-marquardt backpropagation

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A Novel Stochastic Framework for the MHD Generator in Ocean

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Computers, Materials & Continua 2022年第11期73卷 3383-3402页

作者： Sakda Noinang Zulqurnain Sabir Shumaila Javeed Muhammad Asif Zahoor Raja Dostdar Ali Wajaree Weera Thongchai Botmart Department of Mathematics Statistics and Computer Faculty of ScienceUbon Ratchathani UniversityUbon Ratchathani 34190Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematics Comsats University Islamabad45550 Islamabad CampusIslamabadPakistan Future Technology Research Center National Yunlin University of Science and TechnologyYunlin 64002Taiwan Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen 40002Thailand

This work aims to study the nonlinear ordinary differential equations(ODEs)system of magnetohydrodynamic(MHD)past over an inclined plate using levenberg-marquardt backpropagation neural networks(LMBNNs).The stochastic procedures LMBNNs are provided with three categories of sample statistics,testing,training,and *** nonlinear MHD system past over an inclined plate is divided into three profiles,dimensionless momentum,species(salinity),and energy(heat)*** data is applied 15%,10%,and 75%for validation,testing,and training to solve the nonlinear system of MHD past over an inclined plate.A reference data set is designed to compare the obtained and proposed solutions for the MHD *** plots of the absolute error(AE)are provided to check the accuracy and precision of the considered nonlinear system of *** obtained numerical solutions of the nonlinear magnetohydrodynamic system have been considered to reduce the mean square error(MSE).For the capability,dependability,and aptitude of the stochastic LMBNNs procedure,the numerical performances are provided to authenticate the relative arrangements of MSE,error histograms(EHs),state transitions(STs),correlation,and regression.

关键词： MHD energy salinity levenberg-marquardt backpropagation Soret number nonlinear

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Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

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Computers, Materials & Continua 2022年第9期72卷 5015-5030页

作者： Prem Junswang Zulqurnain Sabir Muhammad Asif Zahoor Raja Waleed Adel Thongchai Botmart Wajaree Weera Department of Statistics Faculty of ScienceKhon Kaen UniversityKhon Kaen 40002Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Electrical Engineering COMSATS Institute of Information TechnologyAttockPakistan Department of Mathematics and Engineering Physics Faculty of EngineeringMansoura UniversityEgypt UniversitéFrançaise D’Egypte Ismailia Desert RoadEl-ShoroukCairoEgypt Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen 40002Thailand

The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented *** method is constructed with the combination of the ANNs along with the levenberg-marquardt backpropagation(LMB),named the *** technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference *** numbers neurons have been used to solve the fractional-order chaotic financial *** selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for *** results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and *** obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).

关键词： Financial model chaotic fractional-order reference dataset artificial neural networks levenberg-marquardt backpropagation

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Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

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Computers, Materials & Continua 2023年第2期74卷 2575-2588页

作者： Sakda Noinang Zulqurnain Sabir Muhammad Asif Zahoor Raja Soheil Salahshour Wajaree Weera Thongchai Botmart Department of Mathematics Statistics and Computer Faculty of ScienceUbon Ratchathani UniversityUbon Ratchathani34190Thailand Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan Faculty of Engineering and Natural Sciences Bahcesehir UniversityIstanbul34494Turkey Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the levenberg-marquardt backpropagation(LMB)neural networks(NNs),i.e.,*** FO-HBV-DIS with the response of antibody immune is categorized into five dynamics,healthy hepatocytes(H),capsids(D),infected hepatocytes(I),free virus(V)and antibodies(W).The investigations for three different FO variants have been tested numerically to solve the nonlinear *** data magnitudes are implemented 75%for training,10%for certification and 15%for testing to solve the FO-HBV-DIS with the response of antibody *** numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton *** authenticate the validity,competence,consistency,capability and exactness of the LMBNNs,the numerical presentations using the mean square error(MSE),error histograms(EHs),state transitions(STs),correlation and regression are accomplished.

关键词： Fractional order HBV differential infection system artificial neural networks nonlinear levenberg-marquardt backpropagation Adams-Bashforth-Moulton

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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

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Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

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Computers, Materials & Continua 2023年第2期74卷 2415-2430页

作者： Narongsak Yotha Qusain Hiader Zulqurnain Sabir Muhammad Asif Zahoor Raja Salem Ben Said Qasem Al-Mdallal Thongchai Botmart Wajaree Weera Department of Applied Mathematics and Statistics Rajamangala University of Technology IsanNakhon Ratchasima30000Thailand Department of Mathematics University of GujratGujrat50700Pakistan Department of Mathematics Hazara UniversityMansehra21120Pakistan Future Technology Research Center National Yunlin University of Science and TechnologyDouliouYunlin64002Taiwan Department of Mathematical Science College of ScienceUnited Arab Emirates UniversityAl AinAbu DhabiUAE Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

This study aims to solve the nonlinear fractional-order mathematical model(FOMM)by using the normal and dysregulated bone remodeling of themyeloma bone disease(MBD).For themore precise performance of the model,fractional-order derivatives have been used to solve the disease model *** FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts(OC)and bone formation or osteoblasts(OB).The connections of OC and OB are represented by a nonlinear differential system based on the cellular components,which depict stable fluctuation in the usual bone case and unstable fluctuation through the *** myeloma causes by increasing the OC and reducing the osteoblasts,resulting in net bone waste the tumor *** solutions of the FOMM will be provided by using the stochastic framework based on the levenberg-marquardt backpropagation(LVMBP)neural networks(NN),i.e.,*** mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the *** static structural performances are 82%for investigation and 9%for both learning and *** performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton *** accomplish the capability,steadiness,accuracy,and ability of the LVMBPNN,the performances of the error histograms(EHs),mean square error(MSE),recurrence,and state transitions(STs)will be provided.

关键词： Bone remodeling fractional-order myeloma disease artificial neural networks levenberg-marquardt backpropagation population cell dynamics

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An Intelligence Computational Approach for the Fractional 4D Chaotic Financial Model

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Computers, Materials & Continua 2023年第2期74卷 2711-2724页

作者： Wajaree Weera Thongchai Botmart Charuwat Chantawat Zulqurnain Sabir Waleed Adel Muhammad Asif Zahoor Raja Muhammad Kristiawan Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematical Sciences United Arab Emirates UniversityP.O.Box 15551Al AinUAE Department of Mathematics and Engineering Physics Faculty of EngineeringMansoura UniversityEgypt UniversitéFrançaise D’Egypte Ismailia Desert RoadEl-ShoroukCairoEgypt Future Technology Research Center National Yunlin University of Science and Technology123 University RoadSection 3DouliouYunlin 64002Taiwan Science of Education Universitas BengkuluBengkulu CityIndonesia

The main purpose of the study is to present a numerical approach to investigate the numerical performances of the fractional 4-D chaotic financial system using a stochastic *** stochastic procedures mainly depend on the combination of the artificial neural network(ANNs)along with the levenberg-marquardt backpropagation(LMB)i.e.,ANNs-LMB *** fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional orderα.The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and *** data proportion is applied as 73%,15%,and 12%for training,testing,and certification to solve the chaotic fractional *** acquired results are verified through the comparison of the reference solution,which indicates the proposed technique is efficient and *** 4-D chaotic model is numerically solved by using the ANNs-LMB technique to reduce the mean square error(MSE).To authenticate the exactness,and consistency of the technique,the obtained performances are plotted in the figures of correlation measures,error histograms,and *** these figures,it can be witnessed that the provided technique is effective for solving such models to give some new insight into the physical behavior of the model.

关键词： Financial model chaotic levenberg-marquardt backpropagation fractional order artificial neural networks reference dataset

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Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

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Computers, Materials & Continua 2023年第3期 5915-5930页

作者： Naret Ruttanaprommarin Zulqurnain Sabir Rafaél Artidoro Sandoval Nez Emad Az-Zo’bi Wajaree Weera Thongchai Botmart Chantapish Zamart Department of Science and Mathematics Faculty of Industry and TechnologyRajamangala University of Technology Isan Sakonnakhon CampusSakonnakhon47160Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematical Sciences United Arab Emirates UniversityP.O.Box 15551Al AinUAE Universidad Nacional Autonoma de Chota CajamarcaPeru Department of Mathematics and Statistics Mutah UniversityMutah-Al Karak-Jordan Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on levenberg-marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

关键词： Holling 3^(rd)type delay factor mathematical model neural networks levenberg-marquardt backpropagation

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