Search Results (2,047)

This paper investigates a class of coupled $\psi$-Hilfer fractional pantograph–Langevin equations with nonlocal integral boundary conditions. By reformulating the problem as an equivalent fixed point equation and employing Mönch’s fixed point theorem together with the Kuratowski measure of noncompactness, we establish sufficient conditions for the existence of at least one solution. Under additional Lipschitz-type assumptions, we prove Ulam–Hyers stability on a suitable closed ball and derive explicit, computable stability constants. A concrete numerical example is presented in which all hypotheses are verified and the stability constants are explicitly computed (e.g., $K_1\approx 3.811$, $K_2\approx 2.761$), illustrating the applicability of the theoretical results. The study contributes additional qualitative results to the analysis of fractional pantograph–Langevin systems within the unified framework of $\psi$-Hilfer fractional derivatives. Full article

Background/Objectives: African American (Black) prostate cancer (PCa) patients have a higher risk of dying from the disease and are less likely to undergo radical treatment than European Americans (White). The disparities in PCa-specific mortality (PCSM) and mortality rate (PCSMR) vary geographically. This study investigated the impact of treatments on PCSM, PCSMR and the relevant disparities. Methods: Using the Cox PH model and other statistical methods, we analyzed two datasets extracted from the SEER and PLCO databases. The SEER dataset contains 650,754 White patients and 113,598 Black patients. The PLCO dataset included 7463 Whites and 495 Blacks, and supplemented the SEER data with information on PCa family history (pros_fh). Results: Analysis of SEER data showed that the relative mortality risk (RR) of patients undergoing surgery alone was significantly lower than that of patients receiving radiotherapy alone or a combination of surgery and radiotherapy. Black patients’ RR estimated by the model including treatment was substantially smaller than that estimated by the reduced model excluding treatment. The differences between Black and White in the three-nine-year PCSMR of patients with high-grade or non-localized cancer were significantly correlated with the differences in surgery alone rate (r < −0.65, p < 0.001). Regression-based mediation analysis indicated that treatment disparity had a significant direct effect on mortality disparity and did not mediate the effect of age disparity. Analysis of PLCO data showed that pros_fh had no significant effect on survival but confirmed the survival advantage of surgery over radiotherapy. Conclusions: The results of this study support the hypothesis that, for PCa patients in the United States, geographic variation in treatment disparities partially explains variation in mortality disparities. Full article

In this paper, we investigate the properties of the boundedness of fractional integral operators $K_{\alpha }$ defined on general measure metric spaces. We study their action in Lebesgue spaces $L^p\left(Y\right)$, Morrey spaces $L_{\phi }^p\left(Y\right)$, and extend our analysis to fractional Sobolev spaces $W^{\alpha ,p}\left(Y\right)$. Using classical dyadic decomposition and the Hardy–Littlewood maximal operator, we establish sharp bounds for $K_{\alpha }$ in terms of kernel parameters and the geometric structure of the space. A significant contribution of this work is the proof that $K_{\alpha }$ is bounded from $W^{\alpha ,p}\left(Y\right)$ to $L^q\left(Y\right)$, where thus linking our operator-theoretic framework with the theory of nonlocal and fractional partial differential equations. These results provide valuable tools for studying regularity, a priori estimates, and solution mappings in nonlocal problems involving the fractional Laplacian and related operators on irregular or non- Euclidean domains. Full article

This paper presents a comprehensive study on constructing exact and approximate solutions to Cauchy problems for time-fractional systems with variable coefficients. An innovative iterative approach is developed for solving functional equations with initial conditions, combining rigorous mathematical foundations with practical computational efficiency. The proposed technique effectively handles the nonlocal nature of fractional operators through a carefully designed iterative scheme that maintains simplicity while achieving high accuracy. It demonstrates particular strength in solving nonlinear systems with well-defined conditions and variable coefficients, where traditional methods often fail. Through systematic theoretical analysis and numerical validation, we establish the method’s convergence properties and computational advantages, showing its capability to generate both exact closed-form solutions, when available, and high-precision approximations otherwise. The approach remains computationally tractable even for complex cases where variable coefficients and memory effects of fractional systems present significant challenges to conventional solution approaches. Full article

This study examines a comprehensive class of coupled nonlinear $\varrho$-Hilfer fractional neutral impulsive integro-differential systems with mixed delays and non-local initial conditions. The primary contribution of this study is the creation of a unified analytical framework that encompasses coupled interactions, neutral-type dependencies, and impulsive disturbances, which have been studied separately by researchers. We utilize the Banach contraction principle and Krasnoselskii’s fixed-point theorem to provide suitable conditions for the existence and uniqueness of solutions within the product space of piecewise continuous weighted functions. In addition to existence, we examine Ulam–Hyers–Rassias (UHR) stability using a generalized Gronwall inequality, which guarantees the system’s robustness against functional perturbations. We also develop a controllability framework and a feedback control law that steer the system towards the desired terminal states. The theoretical results are supported by a numerical simulation using a complex kernel, implemented via a modified predictor-corrector algorithm, which validates the practical effectiveness of the proposed control and stability outcomes. Full article

The Copenhagen Interpretation of quantum mechanics explains the Einstein, Podolsky, and Rosen (EPR) experiments with “spooky action at a distance” and nonlocal wavefunction collapse. A time-symmetric and retrocausal interpretation of quantum mechanics explains the same experiments without spooky action at a distance or nonlocal wavefunction collapse. An experiment that can distinguish between the Copenhagen and Time-Symmetric Interpretations is described. Full article

This work constructs an orthogonal function system on bounded intervals $[0,R]$ associated with the Atangana–Baleanu–Caputo (ABC) fractional derivative for $\alpha \in (1/2,1)$. Starting from a fractional Laguerre-type equation involving the ABC operator, solutions are obtained via a generalized Frobenius method, yielding series representations with characteristic exponent $\alpha -1$. Rather than postulating a weight function by analogy with classical or Caputo settings, the weight is derived directly from the requirement that the underlying fractional operator be formally self-adjoint on a suitable admissible domain. This operator-theoretic approach leads to the explicit Mittag–Leffler weight $w_{\alpha }\left(x\right)=x^{-(2\alpha -1)}{E}_{\alpha }(-x^{\alpha })$, which intrinsically reflects the nonlocal memory structure of the ABC kernel. A similarity transformation removes the universal singular factor and produces regularized eigenfunctions that are continuous on $[0,R]$ and orthogonal in the weighted $L^2$ space. The weight identity and formal self-adjointness are rigorously verified through a right-Volterra uniqueness argument. Numerical experiments confirm orthogonality up to machine precision, demonstrate spectral convergence for a model ABC differential equation, and illustrate consistency with classical Laguerre polynomials in the limit $\alpha \to 1^{-}$. The resulting framework provides a self-consistent orthogonal system suitable for spectral approximations of problems governed by the ABC operator on bounded domains. Full article

This paper investigates the optimal investment and reinsurance problem for insurers in a financial market with contagion risk. The prices of risky assets are assumed to follow a jump–diffusion model, where the jump component is driven by a multidimensional dynamic contagion process with diffusion (DCPD). This process simultaneously captures jumps triggered by endogenous and exogenous excitations, effectively characterizing the dynamic contagion effects arising from the joint influence of multiple factors in financial markets. The insurer aims to maximize a mean-variance (MV) utility function by purchasing per-loss reinsurance and investing the surplus in the contagion financial market. By solving the extended Hamilton–Jacobi–Bellman (HJB) equations, we derive the time-consistent equilibrium investment and reinsurance strategies, as well as explicit expressions for the equilibrium value function. These results are characterized by two nonlocal partial differential equations (PDEs), whose probabilistic solutions are obtained through the Feynman–Kac formula. Finally, numerical experiments illustrate how equilibrium strategies respond to changes in contagion intensity and confirm the effectiveness of the proposed model. Full article

This paper focuses on establishing the existence of infinitely many solutions for non-local fractional equations characterized by unbalanced growth and Hardy potentials. We prove that these solutions converge to zero in the $L^{\infty }$-norm, requiring conditions on the nonlinearity only near the origin and dispensing with assumptions at infinity. As far as we are aware, results for non-local fractional $(p,q)$-Laplacian problems with singular coefficients such as Hardy potentials have not been extensively studied. To address this gap, we employ the dual fountain theorem together with the modified functional method. Full article

Background: Vaccines targeting herpes zoster, influenza, and pneumococcal diseases represent the most effective interventions for reducing morbidity and mortality in individuals aged ≥65 years. This study employs real-world vaccination data for herpes zoster vaccine (HZV), influenza vaccine (InfV), and 23-valent pneumococcal polysaccharide vaccine (PPSV23) among individuals aged ≥60 years in the Pudong New Area of Shanghai, China, from 2020 to 2024, aiming to assess the vaccination coverage for the three vaccines. Methods: Demographic data and vaccination records for HZV, InfV, and PPSV23 were obtained from the Shanghai Immunization Information System. Vaccination coverage, temporal trends, and disparities across different demographic groups and subdistricts or towns were analyzed. Results: From 2020 to 2024, a total of 26,227 doses of HZV, 198,373 doses of InfV, and 102,644 doses of PPSV23 were administered to adults aged ≥60 years in the Pudong New Area of Shanghai, with vaccination coverage of 0.23%, 3.12%, and 1.61%, respectively. HZV coverage peaked in 2023 (0.34%), whereas the highest coverage for InfV (3.94%) and PPSV23 (3.21%) occurred in 2020. The highest vaccination coverage was observed in the 70–74 age group for HZV (0.30%), the 75–79 age group for InfV (5.18%), and the 65–69 age group for PPSV23 (2.15%). Coverage for HZV and InfV was higher among females than males, while PPSV23 coverage was higher among males. Individuals with local household registration had significantly higher coverage for all three vaccines compared to those with non-local registration. The subdistricts or towns with the highest HZV coverage were Jinqiao Town (0.59%), Huamu Subdistrict (0.50%), and Lujiazui Subdistrict (0.34%). For InfV, the highest coverage was observed in Tangqiao Subdistrict (5.50%), Huamu Subdistrict (5.46%), and Lujiazui Subdistrict (4.88%). For PPSV23, the top three were Laogang Town (2.79%), Nicheng Town (2.01%), and Datuan Town (1.93%). Significant spatial clustering was observed for HZV and InfV. Conclusions: Vaccination coverage for HZV, InfV, and PPSV23 among adults aged ≥60 years in the Pudong New Area of Shanghai from 2020 to 2024 was generally low, with evident temporal variations and demographic and spatial disparities. Coverage differed by age group, gender, household registration status, and subdistricts or towns. These findings indicate that future interventions are still needed to increase vaccination coverage among older adults. Full article

This work focuses on the analysis of a sequential fractional boundary value problem involving coupled Erdélyi–Kober and Caputo fractional differential operators, together with nonlocal boundary conditions of fractional type. The well-posedness of the problem is addressed by deriving conditions that ensure the existence and uniqueness of solutions. Uniqueness is obtained through an application of Banach’s contraction principle, whereas existence is established by employing Krasnosel’skiĭ’s fixed point approach and the nonlinear alternative of Leray–Schauder. Several numerical examples are presented to demonstrate and support the theoretical findings. Full article

We present a covariant geometric extension of General Relativity formulated within a controlled effective field theory framework. The gravitational action is supplemented by curvature-dependent operators parametrized by three coefficients $\alpha$, $\beta$, and $\gamma$, chosen such that the resulting field equations remain second order in time derivatives and free of Ostrogradsky instabilities. In a homogeneous and isotropic cosmological background, the modified dynamics generically replaces the classical Big Bang singularity with a smooth, nonsingular bounce driven by a repulsive curvature core proportional to $a^{-6}$. A distinctive feature of the framework is the presence of a geometric slip term proportional to $\dot{H}$, which encodes curvature-memory effects at the level of the background evolution without introducing additional propagating degrees of freedom. This term dynamically correlates the expansion rate with its temporal variation, leading to effective ultraviolet damping and enhanced dynamical stability across the high-curvature regime. As a consequence, the cosmological solutions admit the definition of an intrinsic relational time variable that is strictly monotonic throughout the evolution, including across the bounce. The emergent temporal ordering arises purely from geometric dynamics and does not rely on matter clocks, nonlocality, or fundamental violations of time-reversal or CPT symmetry. We discuss the consistency of the framework within its effective field theory domain of validity and comment on its implications for the conceptual problems of singularity resolution and the emergence of time in cosmology. Full article

Infrared small target detection (IRSTD) is a fundamental task in remote sensing-based surveillance and early warning systems. However, extremely small target size, low signal-to-noise ratio, and complex background clutter make reliable detection highly challenging. To address these issues, we propose a Hierarchical Perception Fusion Network (HPFNet) for IRSTD. Specifically, the Patch-Wise Context Feature Extraction module (PCFE) jointly integrates the Patch Nonlocal Block, convolutional blocks and attention mechanism to enable global–local feature extraction and enhancement, thereby strengthening weak target representations. In addition, the Multi-Level Sparse Cross-Fusion module (MSCF) explicitly performs cross-level feature interaction between encoder and decoder representations, enabling effective fusion of low-level spatial details and high-level semantic cues. A dual Top-K sparsification mechanism is adopted to filters’ irrelevant background features, enabling the attention mechanism to focus more on the target region and thereby bolstering the discriminative power of feature representation. Finally, the Efficient Upsampling Module (EUM) combines upsampling with multi-branch dilated convolutions to enhance feature reconstruction and improve localization accuracy. Extensive experiments on publicly available benchmark datasets demonstrate that HPFNet consistently outperforms existing state-of-the-art IRSTD methods. Full article

This manuscript presents a study of the Stress-Driven integral Model (SDM) for the bending response of Bernoulli–Euler nanobeams. Unlike conventional approaches that reformulate the nonlocal integral problem into an equivalent differential form, a direct numerical strategy is developed to solve the integral equation. The proposed framework enables a systematic comparison of six different convolution kernels (Helmholtz, Gaussian, Lorentzian, triangular, Bessel and hyperbolic cosine), highlighting how their mathematical properties influence the structural response. To address issues related to long-range interactions and the potential ill-posedness of the integral operator, an adaptive regularization procedure based on the Morozov discrepancy principle is introduced. Furthermore, a local clipping and renormalization technique is proposed to properly account for boundary effects while preserving the weighted averaging property of the kernels. Validation against available analytical solutions for the Helmholtz kernel demonstrates high accuracy, with errors below 1%. The results show that the nonlocal parameter significantly affects structural rigidity depending on the kernel shape and that the proposed approach ensures consistent convergence to the local solution as the nonlocal parameter tends to zero. Full article

Wind-driven shear and vertical mixing in the upper meter of the ocean strongly regulate near-surface circulation and buoyant tracer transport, yet direct field observations immediately beneath the air–sea interface remain scarce. We present Lagrangian observations, equipped with an upward-looking Acoustic Doppler Current Profiler (ADCP), collected during 5–7 April 2022 in the Jeju Strait under wind stresses of 0.0006–0.19 Pa. Near-surface shear and turbulence metrics were resolved within the top surface layer (TSL), and a response-time analysis showed that upper-layer shear responded most promptly to wind variability, whereas deeper-layer shear and sea-state metrics adjusted more slowly. Wave-period variability exhibited the weakest coupling, indicating additional nonlocal influences. Reynolds-stress estimates showed that the along-wind momentum flux was predominantly negative, indicating net downward transfer of downwind momentum, while cross-direction fluxes were smaller on average and frequently reversed sign, consistent with intermittent lateral transfers associated with evolving wave–current interactions. Using an eddy-viscosity framework, we derived stress-based exponential-saturation parameterizations for depth-averaged shear and vertical diffusivity, with the diffusivity magnitude treated as sensitive to the assumed turbulent Prandtl number. The relationships are intended for event-scale conditions within the observed forcing range and provide field-constrained, implementation-ready formulations for near-surface transport and mixing models. Full article