We aim to detect outliers in the daily stock price indices from the Saudi Arabia stock exchange (Tadawul) with 2026 observations from October 2011 to December 2019 provided by the Saudi Authority for Statistics and the Saudi Central Bank. We apply the Multi-Layer Perceptron (MLP) algorithm for detecting outliers in stock returns. We select the inflation rate (Inflation), oil price (Loil), and repo rate (Repo) as input variables to the MLP architecture. The performance of the MLP is evaluated using standard metrics for binary classification, namely the false positive rate (FP rate), false negative rate (FN rate), F-measure, Matthews correlation coefficient (MCC), accuracy (ACC), and area under the ROC curve (AUC). The results demonstrate the efficiency and good performance of the MLP algorithm based on different criteria tests.

The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE method combined with Bäcklund transformation and conformable fractional derivatives. The obtained solutions are expressed in trigonometric, hyperbolic, and rational forms, highlighting the adaptability and efficacy of the proposed approach. To enhance the understanding of the results, the solutions are visualized using 2D representations for fractional-order variations and 3D plots for integer-type solutions, supported by detailed contour plots. The findings contribute to a deeper understanding of nonlinear wave–wave interactions and the underlying dynamics governed by fractional-order derivatives. This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling.

This study investigates the fractional-order Sawada–Kotera and Rosenau–Hyman equations, which significantly model non-linear wave phenomena in various scientific fields. We employ two advanced methodologies to obtain analytical solutions: the q-homotopy Mohand transform method (q-HMTM) and the Mohand variational iteration method (MVIM). The fractional derivatives in the equations are expressed using the Caputo operator, which provides a flexible framework for analyzing the dynamics of fractional systems. By leveraging these methods, we derive diverse types of solutions, including hyperbolic, trigonometric, and rational forms, illustrating the effectiveness of the techniques in addressing complex fractional models. Numerical simulations and graphical representations are provided to validate the accuracy and applicability of derived solutions. Special attention is given to the influence of the fractional parameter on behavior of the solution behavior, highlighting its role in controlling diffusion and wave propagation. The findings underscore the potential of q-HMTM and MVIM as robust tools for solving non-linear fractional differential equations. They offer insights into their practical implications in fluid dynamics, wave mechanics, and other applications governed by fractional-order models.

The expansion of the application domains is greatly aided by the generalization of distributions. To achieve this, an extension of the two–parameter Kumaraswamy distribution to a three–parameter second order transmuted Kumaraswamy distribution has been presented in this study utilizing the cubic transmutation map. Along with the order statistics and parameter estimates, a number of statistical characteristics are shown. The performance of the estimated parameters has been demonstrated through simulation study. A few applications additionally serve to demonstrate the suggested distribution’s dominating applicability.

When extreme values or outliers occur in asymmetric datasets, conventional mean estimation methods suffer from low accuracy and reliability. This study introduces a novel class of robust Särndal-type mean estimators utilizing re-descending M-estimator coefficients. These estimators effectively combine the benefits of robust regression techniques and the integration of extreme values to improve mean estimation accuracy under simple random sampling. The proposed methodology leverages distinct re-descending coefficients from prior studies. Performance evaluation is conducted using three real-world datasets and three synthetically generated datasets containing outliers, with results indicating superior performance of the proposed estimators in terms of mean squared error (MSE) and percentage relative efficiency (PRE). Hence, the robustness, adaptability, and practical importance of these estimators are illustrated by these findings for survey sampling and more generally for data-intensive contexts.