This study rigorously investigates the asymptotic dynamics of systems governed by the space–time conformable Von Foerster–Lasota partial differential equation of order $ \kappa \in (0, 1) $, where both the temporal and spatial variables are defined in the conformable sense. We establish sufficient conditions for the emergence of Devaney chaos and provide a detailed analysis of the strong stability of the associated solution $ \kappa $-semigroup within Orlicz spaces induced by a convex $ \Psi $-function. By employing Matuszewska–Orlicz indices, we offer a precise characterization of the long-term behavior of the generated $ \kappa $-semigroup. Notably, this work bridges the gap between the studies of Dawidowicz and Poskrobko (2016), who considered Orlicz spaces for classical derivatives, and Elkhalloufy et al. (2025), who investigated conformable equations in Lebesgue spaces. By extending the conformable framework to the more general setting of Orlicz spaces, we offer new insights into the interplay between chaotic dynamics and stability in structured population models.

We propose an LP-Newton-type method for linear programming (LP) with box constraints. In the standard LP-Newton method, each iteration computes a separating hyperplane using the Wolfe algorithm to find the minimum-norm point in a convex polytope. Because this inner routine can be computationally expensive in the worst case (and the Wolfe algorithm may require exponential time), we replace it with a simpler procedure that separates the origin from the convex hull of projected points. This change retains the Newton-type iterative framework while avoiding a potentially intractable inner routine, because the separating hyperplane can be constructed much more efficiently. We also derive an upper bound on the number of iterations. In our experiments, the resulting Naive Separation Algorithm (NSA) ran faster in some settings than the simplex method, which is often cited as one of the Top 10 Algorithms of the 20th Century [1]. These results suggest that this direction may lead to efficient algorithms for box-constrained LP.

In this paper, we established a time-varying latent factor model with GARCH (generalized autoregressive conditional heteroskedasticity) noise to study volatilities (conditional covariance matrix) under the high-dimensional framework, when factors are unobservable, factor loadings are time-varying, and the idiosyncratic error term shows heteroskedasticity. A projection method was proposed for more-precise estimation of the conditional covariance matrix. We demonstrated that our model is robust when the dimensionality and sample size are large. Asymptotic theories were developed for the proposed estimation. A simulation study was conducted to evaluate the performance of the proposed model, and a real example was provided to illustrate this approach.

This study presents a neural network-based framework for finding approximate series solutions to Abel's integral equation (AIE) and fractional order Volterra-type integro-differential equations (FOVIDEs). The suggested method changes the problem by writing the solution as a power series that has been truncated. This makes the original differential equation a problem of estimating parameters. Then, a special neural network is trained to find the coefficients of the series with good accuracy. Numerical tests show that the proposed method works, maintains accuracy, and converges. This shows that it can be used as a strong computational tool for solving fractional order systems.

This paper studies the analytical and dynamical behavior of a generalized (3+1)-dimensional extended Kadomtsev-Petviashvili (eKP) equation, which includes higher-order nonlinear and dispersive effects. Using the exp$ (-\varphi(\xi)) $-expansion method, exact traveling wave solutions are obtained successfully. The solutions exhibit rich nonlinear wave structures, including localized solitons, periodic waves, and breathing patterns. To further explore the qualitative behavior of the system, a reduction of traveling waves is used, resulting in a planar dynamical system. A bifurcation analysis is carried out in detail by investigating the equilibrium points, Jacobian structures, and their relations to system parameters. The phase portraits show topological transitions such as centers, saddles, and cusp points. Moreover, a perturbed form of the reduced system is considered in order to investigate chaotic dynamics under periodic external forcing. The existence of chaos is verified using bifurcation diagrams, sensitivity analysis, Poincaré maps, time series, and both 2D and 3D phase portraits. These numerical simulations confirm the theoretical predictions and demonstrate the system's complex behavior across varying perturbation parameters. Overall, the outcomes provide a complete picture of the soliton structures and chaotic regimes that the eKP model may exhibit in physico-nonlinear wave propagation in multidimensional contexts.

We propose the Frailty-Augmented Logistic-Weighted Lomax Mixture (F-LLoM), a finite-mixture survival model that combines gamma frailty within components with covariate-dependent multinomial logistic mixing weights. After integrating out the frailty, each component follows a Lomax (Pareto II) distribution, enabling flexible modeling of heavy-tailed survival times and latent heterogeneity, while covariates affect both tier membership and within-tier hazard scales. We derive identifiability conditions, moment expressions, and tail properties, and develop a censoring-aware expectation–maximization (EM) algorithm for right-censored data. In simulation studies with sample sizes between 500 and 1000 and censoring rates up to 20%, the Bayesian information criterion consistently selected the true number of components, and the EM algorithm showed stable convergence with well-calibrated predictions. An application to the Rossi recidivism dataset illustrates the practical implementation of the model and favors a parsimonious specification. The proposed framework provides a practical and interpretable approach for analyzing heterogeneous and heavy-tailed survival data.

For the biased random walk on $ d $-regular trees, we obtain the spectral radius, first return probability and $ n $-step transition probability, speed. We prove that the spectral radius depends continuously on the bias parameter and is strictly increasing with respect to it, while the speed remains strictly positive and decreases monotonically as the bias increases.

This research investigated the different types of exact soliton solutions of the biomathematics model known as the truncated M-fractional Heimburg model. This concerned equation describes the transmission of electromechanical pulses in nerves as well as to describe the flow of blood through blood vessels. For our purpose, we used the modified extended tanh function scheme and the modified $ (G'/G^2) $-expansion scheme. The obtained exact soliton solutions were the periodic, kink, singular, dark, bright, and other soliton solutions. The obtained solutions were dynamically explained by using 2D, 3D, and contour graphs. The obtained results were nonexistent due to the use of a novel definition of fractional derivatives. Both schemes were not used for the concerned model in the literature. The effect of the fractional derivative on the solutions was explained by using 2D graphs. Next we gained the steady-state solutions with the help of modulation instability analysis. The obtained solutions are useful for various purposes like blood flow simulation, vascular disease modeling, hemodynamic analysis, medical device design, physiological research, etc.

In this paper, we studied the non-resistive axially symmetric Hall-Magnetohydrodynamics (MHD) system. We showed that the lifespan of their strong solutions can be arbitrarily large if their initial magnetic gradient was small enough. Precise lifespan lower bounds for both viscid and inviscid cases were given.

In this paper, we study one class of nonlinear binomial differential equation$ (f(z))^{n}+a(f^{(k)}(z))^{n} = p_{1}e^{\lambda_{1}z}+p_{2}e^{\lambda_{2}z}, $where $ n, k\in \mathbb{N^{+}} $, $ a $, $ p_i $, and $ \lambda_i $ are nonzero constants for $ i = 1, 2 $. Some results answer the previous conjecture given by Linkui Gao and Junyang Gao.