Explicit scheme for solving variable-order time-fractional initial boundary value problems.

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made.

Divorce prediction using machine learning algorithms in Ha'il region, KSA.

The application of artificial intelligence (AI) in predictive analytics is growing in popularity. It has the power to offer ground-breaking solutions for a range of social problems and real world societal difficulties. It is helpful in addressing some of the social issues that today's world seems incapable of solving. One of the most significant phenomena affecting people's lives is divorce. The goal of this paper is to study the use of machine learning algorithms to determine the effectiveness of divorce predictor scale (DPS) and identify the reasons that usually lead to divorce in the scenario of Hail region, KSA. For this purpose, in this study, the DPS, based on Gottman couples therapy, was used to predict divorce by applying different machine learning algorithms. There were 54 items of the DPS used as features or attributes for data collection. In addition to the DPS, a personal information form was utilized to gather participants' personal data in order to conduct this study in a more structured and traditional manner. Out of 148 participants 116 participants were married whereas 32 were divorced. With the use of algorithms artificial neural network (ANN), naïve bayes (NB), and random forest (RF), the effectiveness of DPS was examined in this study. The correlation based feature selection method was used to identify the top six features from the same dataset and the highest accuracy rate was 91.66% with RF. The results show that DPS can predict divorce. This scale can help family counselors and therapists in case formulation and intervention plan development process. Additionally, it may be argued that the Hail region, KSA sampling confirmed the Gottman couples treatment predictors.

Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making problems.

A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.

Analysis of food chain mathematical model under fractal fractional Caputo derivative.

In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.