Breast cancer is one of the common malignancies among females in Saudi Arabia and has also been ranked as the one most prevalent and the number two killer disease in the country. However, the clinical diagnosis process of any disease such as breast cancer, coronary artery diseases, diabetes, COVID-19, among others, is often associated with uncertainty due to the complexity and fuzziness of the process. In this work, a fuzzy neural network expert system with an improved gini index random forest-based feature importance measure algorithm for early diagnosis of breast cancer in Saudi Arabia was proposed to address the uncertainty and ambiguity associated with the diagnosis of breast cancer and also the heavier burden on the overlay of the network nodes of the fuzzy neural network system that often happens due to insignificant features that are used to predict or diagnose the disease. An Improved Gini Index Random Forest-Based Feature Importance Measure Algorithm was used to select the five fittest features of the diagnostic wisconsin breast cancer database out of the 32 features of the dataset. The logistic regression, support vector machine, k-nearest neighbor, random forest, and gaussian naïve bayes learning algorithms were used to develop two sets of classification models. Hence, the classification models with full features (32) and models with the 5 fittest features. The two sets of classification models were evaluated, and the results of the evaluation were compared. The result of the comparison shows that the models with the selected fittest features outperformed their counterparts with full features in terms of accuracy, sensitivity, and sensitivity. Therefore, a fuzzy neural network based expert system was developed with the five selected fittest features and the system achieved 99.33% accuracy, 99.41% sensitivity, and 99.24% specificity. Moreover, based on the comparison of the system developed in this work against the previous works that used fuzzy neural network or other applied artificial intelligence techniques on the same dataset for diagnosis of breast cancer using the same dataset, the system stands to be the best in terms of accuracy, sensitivity, and specificity, respectively. The z test was also conducted, and the test result shows that there is significant accuracy achieved by the system for early diagnosis of breast cancer.

The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag–Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.

Purpose: The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-state physics, etc. Design/methodology/approach: Dirichlet boundary conditions cannot be handled easily by cubic trigonometric B-spline functions. Then, a modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and a numerical algorithm is developed. The proposed algorithm reduced the hyperbolic-type wave equations into a system of first-order ordinary differential equations (ODEs) in time variable. Then, stability-preserving SSP-RK54 scheme and the Thomas algorithm are used to solve the obtained system. The stability of the algorithm is also discussed. Findings: A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from the schemes developed (Abbas et al., 2014; Nazir et al., 2016) and depicts the computational modelling of hyperbolic-type wave equations. Originality/value: To the best of the authors’ knowledge, this technique is novel for solving hyperbolic-type wave equations and the developed algorithm is free from quasi-linearization process and finite difference operators for time derivatives. This algorithm gives better results than the results discussed in literature (Dehghan and Shokri, 2008; Batiha et al., 2007; Mittal and Bhatia, 2013; Jiwari, 2015).

This paper reports conservation laws for highly dispersive optical solitons in birefringent fibers. Three forms of nonlinearities are studied which are Kerr, polynomial and nonlocal laws. Power, linear momentum and Hamiltonian are conserved for these types of nonlinear refractive index.

The goal of the current numerical simulation is to explore the impact of aspect ratio, thermal radiation, and entropy generation on buoyant induced convection in a rectangular box filled with Casson fluid. The vertical boundaries of the box are maintained with different constant thermal distribution. Thermal insulation is executed on horizontal boundaries. The solution is obtained by a finite volume-based iterative method. The results are explored over a range of radiation parameter, Casson fluid parameter, aspect ratio, and Grashof number. The impact of entropy generation is also examined in detail. Thermal stratification occurs for greater values of Casson liquid parameters in the presence of radiation. The kinetic energy grows on rising the values of Casson liquid and radiation parameters. The thermal energy transport declines on growing the values of radiation parameter and it enhances on rising the Casson fluid parameter.

This paper numerically addresses optical dromions and domain walls that are monitored by Kundu – Mukherjee – Naskar equation. The Kundu – Mukherjee – Naskar equation is considered because this model describes the propagation of soliton dynamics in optical fiber communication system. The scheme employed in this work is Laplace – Adomian decomposition type. The accuracy of the scheme is \(O(10^{-8})\) and the physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of both optical dromions and domain walls.