This work introduces a novel framework for analyzing wave propagation in hydro-semiconductors by simultaneously incorporating fractional-order heat conduction, temperature-dependent thermal conductivity, and rotational effects into a unified photo-thermoelastic model. Unlike previous studies that considered these effects separately, the present model couples nonlocal fractional heat transport with variable thermal conductivity in a rotating semiconductor medium. Analytical solutions are obtained using the normal mode method, and numerical results illustrate how fractional derivatives and temperature-dependent conductivity jointly reshape thermal, mechanical, and carrier wave behaviors compared to classical theories. The findings provide new physical insights into nonlocal, memory-driven, and anisotropic transport phenomena in advanced semiconductor systems, which are not captured by conventional thermoelasticity models.

The study explores analytic, geometric and algebaraic properties of two subclasses of analytic functions: the class of Bounded Radius Rotation denoted by ${\mathcal{R}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, and the class of Bounded Boundary Rotation denoted by ${\mathcal{V}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, both associated with strongly Janowski type functions. In particular, we obtain upper bounds for the third-order Hankel determinant $|{\mathcal{H}}_{3,1}f\left(z\right)|$ and concentrate on functions displaying 2- and 3-fold symmetry. We also provide estimates for the initial logarithmic coefficients ${\eta }_1,{\eta }_2,{\eta }_3$ and the Zalcman functional $|t_3^2-t_5|$ for each class. These findings provide fresh insights into the behavior of generalized subclasses of univalent function.

We study products of Toeplitz operators with angular symbols on the Bergman space over the upper half-plane. We establish necessary and sufficient conditions for the product of two such Toeplitz operators to give rise to a Toeplitz operator, especially in case one of the symbols is absolutely continuous or with bounded variation. Our conditions make appeal to Volterra and Fredholm integral equations, and to Duhamel–Mikusiński convolution products as well as to functional equations involving Stieltjes integrals. We illustrate our results by concrete examples showing that there are many angular symbols satisfying our natural conditions and ensuring Toeplitzness of such Toeplitz products.

The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local Lp regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local Lp regularity introduced by Jaffard. We provide its characterization by a supremum of a wide range oriented anisotropic Triebel wavelet coefficients and leaders. In addition, we deduce estimates on the Hausdorff dimension of the set of points where the directional local Lp regularity does not exceed a given value. The obtained results are illustrated by some examples of self-affine cascade functions.

The total number of older persons globally (those aged 60 years and above) was 202 million in 1950; this total multiplied to attain 901 million and is predicted to triple again in 2100. The growth percentage of the elderly population is quickly improving, and the value of their care shall pose a challenging problem in the future. Notably, the number of older persons in the Kingdom of Saudi Arabia (KSA) is fast growing, from 5 percent of the entire population in 2015 to a predicted 20.9% by 2050. The main problem is the KSA's management of the rising problem of age-related Non-Communicable Diseases (NCD). With the escalating dimensions of the population of older persons and increased prevalence of NCD causes of risk, the occurrence of NCDs in KSA will rise, resulting in a proportional increase in the requirement for medical assistance. In this paper, an Artificial Neural Network-Based Approaches for Improved Forecasting of Disability Care Expenditures in an Aging Kingdom of Saudi Arabia Population (ANNFDCE-AKSAP) method is proposed. The main objective of the ANNFDCE-AKSAP method is to create an accurate and scalable forecasting system capable of addressing the Kingdom's evolving disability care needs. Initially, the ANNFDCE-AKSAP technique utilizes a min-max normalization-based data preprocessing model to ensure consistent scaling across variables. Furthermore, the bidirectional variational autoencoder with the self-attention module (BiVAE‐SAM) model forecasts disability care expenses. Finally, the enriched coati osprey algorithm (ECOA)-based hyperparameter selection process is performed to optimize the prediction results of the BiVAE‐SAM method. A wide range of simulations is accomplished to demonstrate the enhanced performance of the ANNFDCE-AKSAP technique, and the results are inspected using several measures. The comparison study of the ANNFDCE-AKSAP technique illustrated the lowest MSE, 0.0128, and MAE, 0.0942, compared to all other methods.