The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources.

This paper proposes a new family of robust estimators of means, depending on the Orthogonalized Gnanadesikan–Kettenring (OGK) covariance matrix. These estimators are computationally feasible and robust replacements of the Minimum Covariance Determinant (MCD) estimator in survey sampling contexts involving auxiliary information. With the growing popularity of outliers in environmental data, as in the case of measuring solar radiation, conventional estimators like the sample mean or the Ordinary Least Squares (OLS) regression-based estimators are both biased and unreliable. The suggested OGK-based exponential-type estimators combine robust measures of location and dispersion and have a considerable advantage in the estimation of the population mean when auxiliary variables such as temperature are highly correlated with the variable of interest. The MSE property of OGK-based estimators is also obtained through a detailed theoretical derivation with the expressions of optimal weights. Performance was further proved using real-world and simulated data on solar radiation, as well as by demonstrating lower MSEs and higher PREs in comparison to MCD-based estimators. These results show that OGK-based estimators are highly efficient and robust in actual and artificially contaminated situations and hence are a good option in robust survey sampling and environmental data analysis.

Accurate modeling of survival data with nonmonotonic hazards is crucial for epidemiology and reliability studies. We introduce the flexible exponential‐type family (FETF) and its parsimonious two‐parameter submodel (the exponential‐type Weibull, ETW) that can capture both bathtub‐shaped and unimodal hazard rates. We derive closed‐form and convergent series representations for key properties, including moments, quantiles, survival and hazard functions, mean residual life, and Shannon entropy, with the mode obtained numerically. Parameters are estimated by maximum likelihood; inference uses the observed Fisher information together with practical guidance on starting values and convergence diagnostics. Application to anonymized COVID‐19 mortality data shows ETW provides a competitive or improved fit relative to several competitors (Weibull, inverse Weibull, transmuted inverse Weibull, and alpha power Weibull), supported by likelihood‐ratio comparisons, relative improvements in information criteria (ΔAIC = −2.59; ΔBIC = −7.51), and favorable goodness‐of‐fit results (KSD = 0.049; parametric bootstrap p > 0.5 reported). Monte Carlo simulations ( B = 1000) quantify estimator bias and MSE across representative parameter settings and demonstrate consistent model‐selection performance. The ETW thus provides a parsimonious, reproducible, and tractable framework for modeling complex survival data.

This paper aiming at the formulation of a parsimonious two-parameter family of lifetime distributions obtained by a simple but flexible exponential-type transformation of an arbitrary baseline CDF (the Flexible Exponential-Type Family, FETF) and study in detail its Exponential-Type Weibull (ETW) special case. The ETW retains analytical tractability while permitting bathtub-shaped and unimodal hazard rate behavior frequently observed in epidemiology and reliability. To theoretically validate the model, we derive key distributional properties, including the probability density function, survival function, and hazard rate. We present maximum-likelihood estimation (MLE): score equations, observed Fisher information, and asymptotic confidence intervals. We address requirements that guarantee negative definiteness and provide explicit formulas for the Hessian (observed information). Monte Carlo simulations evaluating bias, mean squared error, and model selection frequency as well as application to COVID-19 data (n = 106) from Mexican public records are used to empirically validate the performance of the proposed ETW distribution. The ETW consistently performs better than well-known competing models, such as the Weibull and other state-of-the-art distributions, across information requirements and goodness-of-fit metrics. For simulating non-monotonic hazard issues in epidemiology and reliability investigations, the ETW distribution provides a flexible and computationally easy tool.