Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

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. Untreated myeloma causes by increasing the OC and reducing the osteoblasts, resulting in net bone waste the tumor growth. The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation (LVMBP) neural networks (NN), i.e., LVMBPNN. The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN. The static structural performances are 82% for investigation and 9% for both learning and certification. The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism. To 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.

Section: Resultsmentioning

confidence: 99%

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

Yotha¹,

Hiader²,

Sabir³

et al. 2023

“…Recently, stochastic solvers have been presented to solve the fractional dynamical models. Few of them are dynamical nonlinear susceptible infected and quarantine differential model [55], immune-chemotherapeutic treatment for breast cancer [56], nonlinear prey-predator system [57], SIDARTHE COVID-19 pandemic differential model [58], Bagley-Torvik mathematical model [59] and seventh order singular system [60]. It is found that the time FO derivatives have been applied to different conditions in various applications.…”

Section: Novel Stochastic Solvers Featuresmentioning

confidence: 99%

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Botmart¹,

Hiader²,

Sabir³

et al. 2023

Self Cite

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 S h (t), infected humans I h (t), recovered humans R h (t), infected vectors I v (t) , and susceptible vector S v (t) based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.

“…Few of the fractional derivative applications based on the real-world system applications are provided in these references [53][54][55]. Furthermore, the stochastic procedures recently have been used to solve the fractional order models, like infection-based fractional-order nonlinear prey-predator system [56], seventh order singular system [57], fractional-order SIDARTHE COVID-19 pandemic differential model [58], fractional order dynamical nonlinear susceptible infected and quarantine differential model [59], immune-chemotherapeutic treatment for breast cancer [60], Bagley-Torvik mathematical model [61] and fractional infectious disease model [62]. The novel features of the designed stochastic ANNs-LMBA for the fractional order mathematical rape and its control model are designated as:…”

Section: Novel Features and Framework Of The Stochastic Solversmentioning

confidence: 99%

An Artificial Approach for the Fractional Order Rape and Its Control Model

Weera¹,

Sabir²,

Raja³

et al. 2023

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 rape and its control differential system using three different fractional order values is authenticated to perform the correctness of ANNs-LMBA. The data is used to present the rape and its control differential system is designated as 70% for training, 14% for authorization and 16% for testing. The obtained performances of the ANNs-LMBA are compared with the dataset of the Adams-Bashforth-Moulton scheme. To 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).