Hakeem Ullah¹, Mehreen Fiza^1,*, Ilyas Khan^2,*, Abd Allah A. Mosa³, Saeed Islam¹, Abdullah Mohammed⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 277-291, 2023, DOI:10.32604/cmes.2023.022289

Abstract In this paper, we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method (OAFM) for fractional-order equations using the Caputo operator, which is named FOAFM. The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations (FWE). The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM. A rapidly convergent series solution is obtained from FOAFM and is validated by comparison with other results. The… More >

Naret Ruttanaprommarin¹, Zulqurnain Sabir^2,3, Rafaél Artidoro Sandoval Núñez⁴, Emad Az-Zo’bi⁵, Wajaree Weera⁶, Thongchai Botmart^6,*, Chantapish Zamart⁶

CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 5915-5930, 2023, DOI:10.32604/cmc.2023.034362

Abstract The current research aims to implement the numerical results for the Holling third kind of functional response delay differential model utilizing a stochastic framework based on Levenberg-Marquardt backpropagation neural networks (LVMBPNNs). The nonlinear model depends upon three dynamics, prey, predator, and the impact of the recent past. Three different cases based on the delay differential system with the Holling 3^rd type of the functional response have been used to solve through the proposed LVMBPNNs solver. The statistic computing framework is provided by selecting 12%, 11%, and 77% for training, testing, and verification. Thirteen numbers of neurons have been used based… More >

Wajaree Weera¹, Thongchai Botmart^1,*, Charuwat Chantawat¹, Zulqurnain Sabir^2,3, Waleed Adel^4,5, Muhammad Asif Zahoor Raja⁶, Muhammad Kristiawan⁷

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 2711-2724, 2023, DOI:10.32604/cmc.2023.033233

Abstract 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 procedure. The stochastic procedures mainly depend on the combination of the artificial neural network (ANNs) along with the Levenberg-Marquardt Backpropagation (LMB) i.e., ANNs-LMB technique. The fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional order α. The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and 1. The data… More >

Narongsak Yotha¹, Qusain Hiader², Zulqurnain Sabir³, Muhammad Asif Zahoor Raja⁴, Salem Ben Said⁵, Qasem Al-Mdallal⁵, Thongchai Botmart⁶, Wajaree Weera^6,*

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 2415-2430, 2023, DOI:10.32604/cmc.2023.031352

Abstract This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more precise performance of the model, fractional-order derivatives have been used to solve the disease model numerically. The 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 MBD.… More >

Walaa N. Ismail^1,2,*, Hessah A. Alsalamah^3,4, Ebtesam Mohamed²

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 3945-3976, 2023, DOI:10.32604/cmc.2023.031194

Abstract As a result of the increased number of COVID-19 cases, Ensemble Machine Learning (EML) would be an effective tool for combatting this pandemic outbreak. An ensemble of classifiers can improve the performance of single machine learning (ML) classifiers, especially stacking-based ensemble learning. Stacking utilizes heterogeneous-base learners trained in parallel and combines their predictions using a meta-model to determine the final prediction results. However, building an ensemble often causes the model performance to decrease due to the increasing number of learners that are not being properly selected. Therefore, the goal of this paper is to develop and evaluate a generic, data-independent… More >

Wajaree Weera¹, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Salem Ben Said⁴, Maria Emilia Camargo⁵, Chantapish Zamart¹, Thongchai Botmart^1,*

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 3421-3438, 2023, DOI:10.32604/cmc.2023.030996

Abstract The current investigations provide the solutions of the nonlinear fractional order mathematical rape and its control model 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 model. The 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 population. The… More >

Sakda Noinang¹, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Soheil Salahshour⁴, Wajaree Weera^5,*, Thongchai Botmart⁵

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 2575-2588, 2023, DOI:10.32604/cmc.2023.029046

Abstract 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., LMBNNs. The 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 FO-HBV-DIS. The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with… More >

Hassan Khan^1,2, Poom Kumam^3,4,*, Asif Nawaz¹, Qasim Khan¹, Shahbaz Khan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332

Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method… More >

Wajaree Weera¹, Chantapish Zamart¹, Zulqurnain Sabir^2,3, Muhammad Asif Zahoor Raja⁴, Afaf S. Alwabli⁵, S. R. Mahmoud⁶, Supreecha Wongaree⁷, Thongchai Botmart^1,*

CMC-Computers, Materials & Continua, Vol.74, No.1, pp. 1735-1748, 2023, DOI:10.32604/cmc.2023.032950

Abstract 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 model. The dynamics of the NEE model achieves more precise by using the form of the FO derivative. The investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this study. The composition of the FO-NEE model is classified into three classes, execution cost of control, system competence of industrial elements and a new diagnostics technical exclusion cost. The mathematical FO-NEE system is numerically studied… More >

Thongchai Botmart¹, Qusain Hiader², Zulqurnain Sabir³, Muhammad Asif Zahoor Raja⁴, Wajaree Weera^1,*

CMC-Computers, Materials & Continua, Vol.74, No.1, pp. 559-573, 2023, DOI:10.32604/cmc.2023.031871

Abstract The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans , infected humans , recovered… More >