On Some Integral Inequalities via Conformable Fractional Integrals

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

“…Future Research Directions: In the future, the designed stochastic procedure can be executed to solve the higher order systems [47][48][49][50][51][52][53] and biological population systems [54,55].…”

Section: Resultsmentioning

confidence: 99%

Swarming Computational Techniques for the Influenza Disease System

Noinang¹,

Sabir²,

Altamirano³

et al. 2022

The current study relates to designing a swarming computational paradigm to solve the influenza disease system (IDS). The nonlinear system's mathematical form depends upon four classes: susceptible individuals, infected people, recovered individuals and cross-immune people. The solutions of the IDS are provided by using the artificial neural networks (ANNs) together with the swarming computational paradigm-based particle swarm optimization (PSO) and interior-point scheme (IPA) that are the global and local search approaches. The ANNs-PSO-IPA has never been applied to solve the IDS. Instead a merit function in the sense of mean square error is constructed using the differential form of each class of the IDS and then optimized by the PSOIPA. The correctness and accuracy of the scheme are observed to perform the comparative analysis of the obtained IDS results with the Adams solutions (reference solutions). An absolute error in suitable measures shows the precision of the proposed ANNs procedures and the optimization efficiency of the PSOIPA. Furthermore, the reliability and competence of the proposed computing method are enhanced through the statistical performances.

“…In future, the designed ANNs-LMBA can be implemented to solve the fractional kind of derivatives [63][64][65][66][67] and sonic processes [68].…”

Section: Future Research Directionsmentioning

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).