Search Results (1,004)

Triply periodic minimal surface (TPMS) heat exchangers offer high surface-area-to-volume ratios and interconnected flow pathways, making them attractive for compact thermal management. However, accurately predicting nanofluid heat transfer over a wide range of nanoparticle concentrations and operating conditions in complex TPMS geometries remains computationally challenging because of the coupled effects of porous architecture, flow dynamics, and concentration-dependent thermophysical properties. In this study, a hybrid physics-informed neural network (PINN) framework was developed to reconstruct concentration-dependent ${Al}_2{O}_3-water$ nanofluid temperature fields in TPMS gyroid heat exchangers. The originality of the proposed approach lies in integrating sparse thermocouple measurements, a steady-state convection–diffusion equation, boundary condition residuals, concentration-dependent nanofluid property models, and a physics-based concentration scaling procedure within a unified framework. The proposed framework was applied to aluminum and silver TPMS heat exchangers over a wide range of nanofluid volume fractions and flow conditions. The trained PINN accurately reconstructed the experimentally measured temperature field, demonstrating excellent agreement with the reference experimental data. Predictions at concentrations beyond the experimentally measured reference condition were obtained using the physics-based concentration scaling model. The effective heat transfer coefficient and Nusselt number were subsequently evaluated from the predicted mean TPMS temperature through an energy balance formulation. Increasing nanoparticle concentration reduced the predicted TPMS temperatures by approximately 17.5–18.5%, while the combined increase in concentration and flow rate produced an overall temperature reduction of about 33.5%. Relative to the selected baseline condition, the combined variation in concentration and flow rate was associated with calculated increases of 62.08% in $h_{eff}$ , 58.33% in Nu, and 59.32% in Re. These results demonstrate the potential of the proposed hybrid PINN framework as a computationally efficient surrogate for evaluating nanofluid-enhanced TPMS heat exchangers, while acknowledging that predictions away from the training concentration depend on the validity of the concentration scaling model. Full article

We present and analyze a time-fractional, partly diffusive model of two electrically coupled Hindmarsh–Rose neurons in which only the membrane potentials undergo spatial transport, through a nonlinear Neumann m-Laplacian, while the temporal evolution is governed by a Caputo derivative of order $\rho \in (0,1]$. The fractional operator incorporates hereditary relaxation, whereas the m-Laplacian represents gradient-dependent degenerate transport and recovers ordinary diffusion when $m=2$. In a Gelfand triple adapted to the no-flux boundary condition, we derive a fractional energy inequality, a uniform dissipative estimate, and the existence of a global weak solution by a Faedo–Galerkin approximation, fractional compactness, and Minty’s method. Uniqueness and continuous dependence are obtained in the stated bounded solution class. We prove global Mittag–Leffler synchronization above an explicit coupling threshold and establish a practical synchronization bound under parameter mismatch. A fully implicit L1 finite-volume method is then constructed; every time step is solvable, uniqueness follows under an explicit monotonicity condition, and the scheme is unconditionally energy dissipative and convergent. Manufactured-solution tests recover the expected $2-\rho$ temporal and second-order spatial rates. In the neuronal simulations, reducing $\rho$ from 1 to $0.90$ lengthens the mean bursting period from about 379 to 565 time units, an increase of roughly one half, and raises the number of spikes per burst from about $31.7$ to $38.8$. Over $2\le m\le 4$ the temporal rhythm is essentially unchanged, the burst period staying near 362 time units, while the diffusion exponent reshapes the peak amplitude and the spatial gradient profiles of the traveling fronts. The empirical synchronization threshold for the canonical parameter set is approximately $11.0$, far below the global sufficient bound $2.3917\times {10}^4$, which quantifies the conservatism of the analytical certificates. Full article

This study addresses the analysis and numerical solution of a nonlinear time fractional diffusion problem with periodic boundary conditions. A generalized Fourier-based approach is applied to obtain a representation of the solution within a suitable Banach space, taking advantage of the periodic nature of the problem. Existence and uniqueness analysis of the solution is performed under the assumption of coordinated convexity instead of the commonly used global Lipschitz condition on the source term. Furthermore, a finite difference scheme based on the L1 approximation is proposed for the numerical solution of the problem. The consistency of the proposed method is verified through numerical experiments. In addition, the effect of fractional order on the solution behavior is investigated, and the results are supported by theoretical findings. Full article

Synthetic-aperture radar (SAR) ship detection is a fundamental task in maritime remote sensing, supporting wide-area surveillance, traffic monitoring, and emergency response under all-weather imaging conditions. Existing deep detectors mainly rely on spatial cues such as intensity, shape and context, but structured sea clutter and near-shore interference can still produce ship-like responses, while fine scattering details are weakened by deep downsampling. We address two practical representation limitations: incomplete preservation of shallow high-resolution details, and limited explicit modeling of local directional variation. To this end, we propose HMF-RTMDet, a shallow-neck spatial–frequency fusion detector. A P2 high-resolution path combines $C_2$ features with upsampled $P_3$ semantics. HybridMFBlock then processes the fused feature through a morphology branch and a trainable depthwise branch initialized by fractional Gabor templates, followed by channel-wise fusion. In the reported main HRSID run, HMF-RTMDet improves RTMDet-s from 67.9% to 72.6% in AP_50:95, from 90.2% to 94.2% in AP₅₀, and from 68.2% to 73.4% in AP_s. Across three runs, however, its AP_50:95 is 72.17 ± 0.38%, comparable to the SFS-Conv and MCU-only controls. The evidence therefore identifies the P2 path as the main gain source but does not establish a stable advantage for HybridMFBlock over these controls. On SSDD, overall AP_50:95 remains nearly unchanged and large-target performance decreases, defining an important boundary of the current design. Full article

This paper establishes the existence, uniqueness, and Ulam–Hyers stability of solutions for a novel class of coupled sequential hybrid Hilfer fractional q-Duffing equations. By integrating Dhage’s hybrid structure with generalized Hilfer q-operators, we extend recent results on fractional quantum systems. Existence is proven via Dhage’s fixed point theorem in Banach algebras, while uniqueness follows from the Banach contraction principle with explicit verification of operator invariance. All auxiliary functions satisfy rigorous continuity, boundedness, and Lipschitz conditions, and the solution representation is derived with complete calculation of q-integration constants. The theoretical findings are rigorously validated through a detailed numerical example that explicitly verifies all contraction and stability constants. Full article

We study a Caputo fractional three-point boundary value problem of order $\alpha \in (c-1,c]$ and establish three interrelated contributions, all resting on a single refined pointwise ${\mathbf{L}}^2$ estimate for the associated Green function $\mathbf{Gr}(t,s)$. First, we derive a tighter upper bound for ${\sup }_{0<t<1}{\int }_0^1{\mathbf{Gr}}^2(t,s)ds$ by retaining a sign-definite negative mixed term that the classical ${\mathbf{L}}^1$-based analysis of Shivanian discards. The resulting admissible Lipschitz constant ${\kappa }_B$ is explicit in $\alpha$, a, b, c and exceeds Shivanian’s constant ${\kappa }_S$ under an explicit algebraic condition; a closed-form refinement ${\kappa }_B^{\ast }\ge {\kappa }_B$ follows by maximising the pointwise bound in closed form. On Shivanian’s benchmark, the admissible constant rises from $14.646$ to $23.220$ and then to $32.165$. Second, the same contraction constant yields an explicit Ulam–Hyers stability theorem for this problem. While a stability estimate already follows from the classical ${\mathbf{L}}^1$ condition, the refined constant both enlarges the range of admissible Lipschitz constants for which stability is certified and yields a strictly smaller stability constant. Third, we establish quantitative continuous-dependence bounds with respect to the nonlinearity h and the boundary parameter a, and characterize the deterioration of the contraction-based boundary-parameter estimate as the problem approaches resonance. For a fixed Lipschitz constant, this estimate becomes singular as the perturbed contraction factor approaches one and ceases to apply once the contraction condition fails. A more accurate analysis of the Green function thus simultaneously sharpens solvability conditions, stability estimates, and sensitivity bounds for nonlinear Caputo fractional boundary value problems. Full article

Left atrium segmentation from magnetic resonance imaging (MRI) is essential for ablation planning in atrial fibrillation; however, clinical MRI quality is often degraded by noise, artifacts, and incomplete spatial coverage, making traditional recurrent neural networks (RNNs) vulnerable to such distortions. We developed a hybrid architecture inspired by cortico–cerebellar interactions to enhance segmentation stability without compromising mean accuracy. We utilized the open ATRIA dataset (100 patients, isotropic 3D MRI scans with manual left atrium annotations). The model comprises a convolutional encoder, a cortical RNN, and a cerebellar predictive module trained to predict future encoder features across multiple temporal horizons, generating a corrective feedback signal for the RNN. Experiments were conducted on unperturbed and degraded datasets with performance evaluated using the Dice coefficient. On unperturbed data, the cerebellar model achieved a mean best Dice of 0.835 ± 0.032 vs. 0.832 ± 0.027 for the baseline. Under degraded conditions, it showed significantly higher Dice (0.815 ± 0.019 vs. 0.801 ± 0.021; p = 0.014) and Surface Dice (p = 0.040), with a directionally lower between-run variance, though this difference in variance was not formally tested given the limited number of runs. nnU-Net achieved higher absolute accuracy but required three orders of magnitude more inference time and an order of magnitude more parameters. The cerebellar module improved boundary accuracy and reproducibility relative to the non-predictive baseline at a fraction of nnU-Net’s computational cost, offering a lightweight alternative for settings where deploying a full 3D self-configuring model is impractical. Full article

This study examines the microstructural evolution and tensile response of a cold-rolled C17200 Cu–Be–Co alloy strip after short-time annealing at 550 and 610 °C. X-ray diffraction (XRD), electron backscatter diffraction (EBSD), kernel average misorientation (KAM) analysis, transmission electron microscopy (TEM), and room-temperature tensile testing were used to compare phase constitution, grain-boundary character, recrystallization behavior, texture evolution, dislocation substructure, and tensile properties. The results show that both annealed samples mainly consisted of an α-Cu matrix and a small amount of BeCu-related precipitates. After annealing at 550 °C, the alloy retained a recovery-dominated partially recrystallized microstructure, with an average grain size of 1.47 μm, a low-angle grain boundary fraction of 8.4%, a recrystallized fraction of 18.06%, and evident residual dislocation substructures. This condition exhibited a yield strength of 365.5 MPa. After annealing at 610 °C, recrystallization was substantially promoted, the average grain size increased to 1.92 μm, the high-angle grain boundary fraction increased to 97.5%, and the recrystallized fraction reached 82.76%. Meanwhile, the yield strength decreased to 276.6 MPa because of the reduced contribution from dislocation strengthening. These results indicate that, under the two investigated short-time annealing conditions, the strength difference in the alloy is mainly associated with the transition of microstructural evolution from recovery-dominated partial recrystallization to a recrystallization-dominated microstructure. Full article

In this article, a nonlinear coupled system involving Caputo difference operators of distinct orders subject to novel coupled boundary conditions is studied. Existence and uniqueness solutions are established by applying the standard fixed-point theorem under suitable assumptions. The stability behavior of the considered system is analyzed using the Hyers–Ulam stability approach, and sufficient limitations ensuring the stability of the results are obtained. To demonstrate the validity of the theoretical solutions, two illustrative examples are presented. The first example introduces the assumptions required for the existence, uniqueness, and stability results. The second example verifies a financial discrete coupled system solved numerically via a discrete iterative method. Numerical simulations are performed for different fractional orders to examine the influence of memory effects on solution dynamics. Full article

Fractional Brownian motion (fBm) provides a powerful stochastic framework for modeling long-range temporal dependence that cannot be represented by classical Brownian motion. This study presents a numerical and theoretical investigation of constrained fractional Brownian motion with applications to stochastic financial systems. An efficient simulation framework combining Fast Fourier Transform (FFT)-based circulant embedding and Markov Chain Monte Carlo (MCMC) sampling is developed to generate long correlated trajectories under absorbing boundary conditions. The proposed algorithm enables simulations with trajectory lengths up to L = 10⁷ while reducing the computational complexity from O (L³) for direct covariance decomposition to approximately O(L log L). Numerical results accurately reproduce the theoretical autocorrelation function of fBm and confirm the expected persistence behavior governed by the Hurst exponent. Super-diffusive regimes (H > 0.5) exhibit persistent long-range correlations and enhanced survival probabilities, whereas sub-diffusive regimes (H < 0.5) display anti-persistent dynamics and increased boundary absorption. The fractional stochastic volatility formulation captures important characteristics associated with long-memory financial systems, including persistent volatility dynamics and implied-volatility structures. The proposed biophysical-based FFT–MCMC methodology provides an accurate, scalable, and computationally efficient framework for studying constrained fractional stochastic processes and offers a foundation for future investigations of fractional volatility models and related financial applications. A conceptual Adaptive Hurst Momentum framework is briefly discussed as a possible direction for future research. Full article

The Special Issue “Advances in Boundary Value Problems for Fractional Differential Equations—2nd Edition” presents recent advances in the theory and applications of fractional differential equations, fractional inclusions, and systems of fractional differential equations involving Riemann–Liouville, Caputo, Hadamard, Hilfer-Hadamard and other generalized fractional derivatives under a variety of boundary conditions [...] Full article

A spectral Galerkin algorithm is developed for the numerical treatment of modified anomalous time-fractional sub-diffusion equations (MATFSDEs). The algorithm is constructed using Fibonacci coefficient polynomials, from which two space–time trial families are formed. These families are selected so that the homogeneous initial and boundary conditions are automatically incorporated after a suitable transformation of the original problem. The Galerkin formulation then reduces the model to a finite algebraic matrix system whose entries can be explicitly evaluated. To support the construction, inversion, moment, and linearization identities for the selected polynomials are obtained and then used to express the required matrices in closed form. The convergence of the expansion is investigated, and explicit error bounds are derived. Numerical tests are reported to demonstrate the accuracy, applicability, and competitiveness of the proposed scheme in comparison with some existing methods in the literature. Full article

This paper develops a unified qualitative framework for four classes of Liouville–Caputo fractional difference equations arising from different combinations of fractional sums and integer-order differences. Based on the equivalence between initial/final value problems and Volterra-type summation equations, sufficient conditions for the existence and uniqueness of solutions are established by applying the Banach contraction mapping principle together with refined combinatorial estimates. Furthermore, the continuous dependence of solutions on prescribed initial or final data is investigated. By deriving explicit error estimates through a discrete fractional Gronwall-type inequality, we prove that Lipschitz solutions depend continuously on perturbations of boundary data. Numerical experiments for a representative case are presented to verify the theoretical results, including the influence of the fractional order and the sensitivity with respect to boundary data, while additional examples illustrate the applicability of the framework. The obtained results extend the unified discrete fractional calculus framework by providing a rigorous well-posedness analysis and offering a theoretical foundation for further applications of discrete fractional models with memory effects and diverse boundary conditions. Full article

An adaptive immersed boundary method (IBM) for simulating non-isothermal incompressible flows with convective heat transfer involving a rotating circular cylinder is developed. Both Dirichlet- (isothermal) and Neumann (zero heat flux)-type temperature boundary conditions are implemented. In addition to the discrete momentum forcing and energy forcing adopted to effectively satisfy the prescribed velocity and temperature boundary conditions, a mass source/sink term is introduced into the continuity equation to meet the mass conservation at the immersed boundary. The Navier–Stokes equations are solved using the fractional step method implemented on a staggered Cartesian grid system. Time stepping is performed using a second-order Adams–Bashforth/backward-differentiation method, while spatial derivatives are approximated with a second-order centered scheme. Testing of the flow induced by a rotating disk demonstrates that the spatial accuracy of the presented algorithm is second-order. Furthermore, the proposed method is validated by forced convective flow past a rotating isothermal circular cylinder. Finally, mixed Rayleigh–Bénard convection in a square cavity with an embedded adiabatic rotating circular cylinder is simulated, showing that heat transport can be greatly enhanced by increasing the rotating rate and radius of the cylinder at larger Prandtl numbers in the laminar regime. Full article

Thermal therapies require precise prediction of the temperature and stress distributions in skin tissue to ensure efficacy while minimizing tissue damage. Classical bioheat models rely on oversimplified boundary assumptions, such as thermally insulated surfaces and mechanically free membranes, that fail to capture the physiological environment. This study develops a fractional-order dual-phase-lag bioheat model that incorporates clinically realistic conditions, namely simultaneous convective, radiative, and evaporative heat losses, active epidermal cooling, and subcutaneous mechanical restraint modeled through a Winkler elastic foundation. Both the Caputo and the Atangana–Baleanu (ABC) fractional derivatives are employed to represent memory effects in biological tissues. Analytical solutions in the Laplace–Fourier domain are obtained using displacement potential functions, with numerical inversion carried out via the Stehfest algorithm and Gaussian quadrature. The results show that realistic boundary conditions substantially alter the thermomechanical response: convective and evaporative cooling reduce surface temperatures and penetration depths, whereas active cooling permits deeper heating without epidermal damage. The Winkler foundation yields higher compressive stresses than traction-free models, and the ABC operator produces smoother responses than the Caputo operator. Overall, the model reveals the trade-offs between thermal efficacy and mechanical safety, thereby bridging bioheat modeling and clinical practice. Full article