This article investigates the truncated M-fractional Shynaray-IIA equation, which has important applications in many fields, such as fiber optic communication, magnetodynamics of ferromagnetic materials, and fluid dynamics. First, the truncated M-fractional Shynaray-IIA equation is transformed into a nonlinear ordinary differential equation through a fractional-order derivative and the traveling wave transformation. Then, the generalized (G '/G)-expansion method is adopted to get multiple groups of coefficient solutions based on the auxiliary equation. The conditions satisfied by the coefficients of the auxiliary equation are classified, and all novel wave solutions of the TMF-SIIAE are obtained, including bright solitons, dark solitons, and breathers. Finally, in order to better understand the behavior of the solutions, a 3D graph, cartesian and polar graph, contour graph and density graph of the solutions are drawn using Python software. Specifically, we also conducted a comparative analysis between the newly obtained solution and the existing solution, and quantitatively discussed the parameters of fractional-order derivatives and analyzed their physical applications.
In this study, we formulated and analyzed a within-host co-infection model Dengue virus (DENV) and Zika virus (ZIKV) that incorporated CTL-mediated immunity, and four types of distributed time delays. The model described the dynamics of uninfected cells, latently, and productively infected cells for each virus, along with free DENV and ZIKV particles and virus-targeted CTL responses. We first proved that all model solutions remained nonnegative and bounded. We computed the basic reproduction numbers RLD for DENV and RLZ for ZIKV, together with the invasion reproduction numbers RL,inv D and RL,inv Z , which determined invasion capability under pre-existing infection. These numbers governed the existence and the global asymptotic stability of model equilibria. Global stability was established using the Lyapunov method, and numerical simulations were performed to validate the analytical results. In addition, sensitivity analysis identified the most influential parameters affecting viral clearance. The effects of antiviral therapy, time delays, and latent infection stages on the DENV-ZIKV co-dynamics were investigated. The results showed that treatment intervention, prolonged delays, and the inclusion of latent infection stages led to a reduction in RLD and RLZ. Furthermore, neglecting intracellular delays or latent infection stages leads to an overestimation of RLDand RLZand the antiviral efficacy required for infection control. This suggests that therapeutic strategies aimed at prolonging intracellular delay phases and accounting for latent-stage dynamics may decrease these reproduction numbers below unity, thereby promoting viral elimination within the host.
Periodic capillary-gravitational perturbations propagating along the free surface of a heterogeneous liquid were investigated by methods of united perturbation theory. A reduced system of heterogeneous fluid mechanics equations, which takes into account the non-uniformity of the liquid density distribution without considering the physical nature of stratification, was analyzed. The methods of the united theory of regular and singular perturbations in linear approximation were employed to obtain complete dispersion relations that describe the large-scale dynamics and fine structure of periodic flows. Analysis of solution showed that calculated regular functions characterize wave components that determine the large-scale geometry and flow dynamics. Singular functions describe ligament components that determine the fine structure of flows. Moreover, the basic properties of large-scale wave components and ligament fine-structured components were calculated for a liquid with water parameters and different values of the buoyancy frequency in an exponentially stratified liquid. When performing the limiting transition to simpler models, the relations obtained uniformly converged to known expressions for capillary-gravity and internal waves. Singular solutions were lost when the effects of viscosity were neglected in a stratified and homogeneous liquid. A substantial difference of the first constructed complete dispersion relation for periodic gravity-capillary flows from that previously obtained using the Boussinesq approximation is shown.
This paper presents a class of novel, high-order, A-stable defect correction schemes. These schemes are grounded in a newly developed, more versatile class of BDF approaches, which utilize Taylor expansions at time t(n+beta) with beta > 1 being an adjustable parameter. The ranges for the stability parameters of these newly proposed defect correction schemes are specified to ensure A-stability. Additionally, numerical experiments are given to illustrate the precision and robustness of the schemes when addressing stiff problems.
This paper is devoted to the study of mild solutions for the time-fractional Navier-Stokes equations, where the time derivative is interpreted in the Caputo-Hadamard sense. The CaputoHadamard derivative, which involves a logarithmic kernel, is particularly suitable for describing anomalous diffusion processes with ultra-slow dynamics. The main contribution of this work is threefold. First, by reformulating the equations as an abstract Cauchy problem and employing the using Banach fixed point theorem with suitable decay estimates of the linear semigroup generated by the Stokes operator, we established the existence and uniqueness of both global (for sufficiently small initial data) and local (for arbitrarily large initial data) mild solutions in critical Lebesgue spaces. Third, we provided explicit logarithmic decay estimates for these solutions, which reflect the ultra-slow dissipation mechanism induced by the Caputo-Hadamard derivative.
Reliable prediction of financial market movements remains a challenging task due to high volatility, complex interdependencies, and sensitivity to external shocks. This study assessed the performance of advanced machine learning models, including long short-term memory (LSTM), gated recurrent unit (GRU), transformer networks, extreme gradient boosting (XGBoost), and deep multi-layer perceptron (DMLP), as well as proposes their ensemble combinations, in forecasting daily closing prices of five major stock indices (S&P 500, NASDAQ-100, Dow Jones Industrial Average, FTSE 100, and DAX). Results indicate that although all models achieved high predictive accuracy, profitability outcomes varied substantially across models and markets. Among single-model approaches, LSTM generally exhibited more stable positive returns in several indices, while other models showed pronounced variability depending on market conditions. Meanwhile ensemble strategies frequently ranked among the top-performing configurations, often matching or exceeding the performance of adaptive weighting schemes. Performance was strongly index-dependent, with S&P 500 and NASDAQ100 exhibiting comparatively stronger profitability, whereas FTSE and Dow Jones showed weaker and alone is insufficient for profitable trading, underscoring the importance of financial performance metrics, such as total return, drawdown, and risk-adjusted measures, when evaluating predictive models.
In this paper, the (4+1)-dimensional Fokas equation is first reduced to a (2+1)-dimensional bilinear form, and then analyzed by an architecture-guided bilinear neural network method (BNNM) within the Hirota framework. Three representative network topologies, namely the "3-2-1", "3-3-1", and "3-2-3-1" configurations, are used to organize trial functions and derive exact solutions through symbolic coefficient matching. As a result, several families of exact wave patterns are obtained, including lump solutions, lump-stripe-type solutions, lump-soliton-type solutions, and selected degenerate/high-amplitude structures. The comparison among different architectures shows that the hidden-layer depth and the activation composition affect the admissible ansatz forms and the morphology of the resulting interaction profiles for the reduced Fokas equation. The derived solutions are interpreted as prototype wave patterns and analytical benchmarks for localization, interaction, and modulation in multidimensional dispersive media, rather than as experimentally calibrated predictions. In addition, an auxiliary Duffing-based modulation diagnostic is used to visualize the irregular modulation of one selected high-amplitude profile; this comparison is qualitative and does not constitute a rigorous proof that the reduced Fokas equation itself is chaotic. These results show that the BNNM framework provides a structured symbolic route to construct and compare the exact interaction solutions of the reduced Fokas equation.
Interaction dynamics among species yield to Allee effects, spatial memory, and nonlocal competition. When predators are not subject to the Allee effect, the coexistence equilibrium point remains locally asymptotically stable despite nonlocal competition. However, in the presence of the Allee effect, nonlocal competition leads to the destabilization of the coexistence point. Moreover, the model will undergo stability switches, Hopf bifurcation, and Turing bifurcation, and induced complex dynamics will appear. It is also found that when the memory diffusion is small, it has no effect on the stability switches; as it increases, only the nonlocal model exhibits the spatially inhomogeneous Hopf bifurcation. When it exceeds the maximum threshold, this phenomenon occurs in both models. Furthermore, when the memory diffusion coefficient exceeds the threshold, the stability range of the coexistence equilibrium will decrease in both the local and nonlocal models. Finally, numerical simulations verify the theoretical results.
Our aim of this paper was to introduce a new construction of probabilistic Hermite polynomials based on moment generating functions. By using this generating function, we derived several new relations and formulas among the aforementioned polynomials and other types of probabilistic special number sequences and polynomials, such as the probabilistic Stirling numbers of the second kind, probabilistic Bernoulli polynomials of higher order, probabilistic Bernstein polynomials, and probabilistic Euler polynomials of higher order. By selecting special random variables, including Poisson, Uniform, Gamma, Geometric, Exponential, and Normal random variables, we showed that the generating function of probabilistic Hermite polynomials yields distinct and unique generating functions, which lead to new relations among other types of special numbers and polynomials, as presented in the application section of this paper.
Understanding and shaping the dynamics of neural architectures with uncertainty, memory, and spatial interactions is a fundamental problem in neural networks and adaptive systems. In particular, controlled destabilization plays an important role in promoting exploration, adaptability, and non-stationary behavior, yet remains far less studied than stabilization and convergence. In this paper, we investigated destabilizing dynamics in a class of space-time discrete fuzzy multidirectional associative memory (MAM) neural networks with time-varying delays and diffusion effects. Such networks integrate fuzzy rule-based representations, delayed feedback, and spatial coupling, and are relevant to adaptive control, associative memory, and multi-agent dynamical systems. We first established the existence of equilibrium states by using topological degree theory, which provides a rigorous foundation for the subsequent analysis. Then, by designing localized Dirichlet boundary feedback mechanisms and constructing novel discrete Lyapunov-Krasovskii functionals with delay-dependent double-sum terms, we derived verifiable sufficient conditions for global asymptotic and exponential anti-stabilization. These results characterize how diffusion intensity, fuzzy parameters, and self-inhibition coefficients influence destabilizing behavior and determine the rate of divergence from equilibrium. The proposed framework provides new theoretical insights into anti-stabilization dynamics in discrete spatiotemporal fuzzy neural networks. Numerical examples further support the theoretical analysis and demonstrate the effectiveness of the proposed approach.
Usually, convolutional neural networks (CNNs) reduce the features extracted from convolutional layers by adopting the maximum value or arithmetic average method, which is called the pooling process. However, these two pooling methods overlook the spatial dependencies between image features. The Choquet integral is a nonlinear integral, which addresses this limitation by incorporating weighted aggregation via a fuzzy measure, enabling it to effectively model interactions between variables. This capability is essential for processing data with complex dependency structures. Therefore, this paper proposes a novel Choquet integral pooling method for feature extraction in the pooling layer. By conducting experiments on datasets, we demonstrated the effectiveness of the proposed method and compared it with existing techniques. The experimental results indicated that for cases where image features are less prominent and exhibit spatial dependencies, the Choquet integral pooling outperforms traditional pooling methods and demonstrates greater robustness. To ensure the rationality and validity of applying the Choquet integral in CNNs, we conducted a more in-depth study of the Choquet integral based on a copula, that is, the CC-integral, including its averaging, idempotence, translation invariance, and positive homogeneity. This research not only enriches the application fields of the Choquet integral but also provides new theoretical support and technical paths for the research of neural networks.
An enhanced numerical technique for solving the Lane-Emden equation is developed using the spectral homotopy analysis method (SHAM) with Chelyshkov polynomials and Gauss-Lobatto collocation nodes. The numerical results, including absolute errors and comparisons with the exact solution, demonstrate the convergence behavior and accuracy of the proposed approach. The results show that the Chelyshkov-based SHAM provides an effective framework for the numerical treatment of Lane-Emden-type problems.
Forecasting systemic financial risks is crucial for effectively preventing and mitigating such risks. This paper introduces an integrated framework for systemic financial risk forecasting, with its core innovation being the novel combination of phase space reconstruction with delay parameterization (RDPM) and a radial basis function neural network (RBFNN). Based on stock trading data from 41 listed companies in the China A-share stock market, a complex financial network is constructed.
