Vol. 11, No. 1 (2027): Regular Issue

The primary purpose of this study is to develop the impulsive neutral Volterra-Fredholm integro-differential equation using an iterative technique in order to obtain comprehensive analytical results. Using the topological degree technique, we define sufficient and necessary conditions for the existence of solutions to the given dynamical system. To further support these conclusions, we use Gronwall's inequality, which is required for establishing the uniqueness of the solutions under specific situations. Numerical calculations are also used to demonstrate the theoretical findings and assess their precision and applicability. These calculations show how effective the suggested technique is.

Flow-induced vibration (FIV) has traditionally been considered a source of mechanical failure and noise in pipeline systems. However, this study introduces a novel approach that leverages FIV as a diagnostic tool for non-intrusive flow rate estimation using vibration signals and machine learning (ML). A custom-built experimental test rig was developed, comprising a 2-meter PVC pipeline, a controlled centrifugal pump, and both single-axis and triaxial vibration sensors strategically placed along the pipe. This setup enables high-resolution vibration data acquisition under varying flow conditions without penetrating the pipe wall. The novelty lies in a non-intrusive approach and the application of supervised ML algorithms to decode flowrate from structural vibrations---an area that remains inadequately explored in the current literature. Initial polynomial regression analysis of single-axis sensor data revealed strong flow-vibration correlation (R$^2> 0.96$), validating the physical basis for indirect flow measurement. Subsequently, six ML models---including Gradient Boosted Trees and Deep Learning---were trained on multiaxial vibration data, achieving high predictive performance with correlation coefficients up to 0.94 and RMSE as low as 1.81. In a two-class flowrate classification test (32 vs 25 mm$^3$/s), all models demonstrated near-perfect accuracy. This work provides the first integrated experimental-ML framework for real-time, low-cost, and non-intrusive flow monitoring using FIV, offering significant potential for industrial applications where conventional flow meters are impractical.

This study investigates the control problem of a well-established unmanned ground vehicle (UGV) model formulated within the framework of conformable fractional calculus, with particular emphasis on both local and global stability analyses. To demonstrate the effectiveness and robustness of the proposed control strategies, we begin by conducting comprehensive numerical simulations that illustrate the vehicle's behavior under local stability conditions. Subsequently, we extend our analysis to the global domain, where the theoretical results are validated through detailed simulations confirming the system's convergence properties across a wide range of initial states. Furthermore, to clearly distinguish between local and global stability regimes, additional simulations are performed using randomly selected initial conditions—often located significantly far from the equilibrium point. These results highlight the remarkable performance of the proposed nonlinear controllers in ensuring global asymptotic stability. As anticipated, the designed control laws maintain excellent stability characteristics irrespective of the initial configuration, thereby confirming their suitability for practical implementations in real-world UGV navigation and control tasks.

This paper establishes the existence and uniqueness of mild solutions for a novel class of semi-linear fractional integro-differential equations (SFIDEs) of mixed type in a general Banach space $\mathcal{E}$, incorporating non-instantaneous impulses (NIIs) via the conformable fractional derivative ($\mathcal{CFD}$) of order $\var\in(0,1]$. The system features a Volterra-type operator $U$ and a Fredholm-type operator $V$, both embedded in the nonlinear term, capturing hereditary and global spatial effects respectively. Existence and uniqueness are established via the generalized Banach contraction mapping principle, without imposing additional smallness constraints on the contraction constant, while existence alone is obtained through Krasnoselskii's fixed point theorem under a sub-linear growth condition, within a compact $C_0$-semigroup framework. An illustrative example on $L^2([0,1],\mathbb{R})$ is provided to validate the theoretical findings.

This study investigates the synchronization dynamics of neuronal populations in a bilayer Erdős-Rényi (ER) network model with adaptive synaptic plasticity, focusing on the emergence and modulation of Chimera states. By integrating the FitzHugh-Nagumo neuron model with spike-timing-dependent plasticity (STDP) mechanisms, we systematically analyze how inter-layer delays and STDP rules influence the coexistence of synchronous and asynchronous subpopulations. Our key findings reveal three critical contributions: (1) adaptive STDP generates diverse Chimera configurations through dynamic synaptic weight modulation; (2) minute variations in inter-layer delay $\tau$ drive bistable transitions in network coherence; and (3) anti-Hebbian STDP enables full state transitions among synchronous, asynchronous, and non-synchronous regimes, whereas Hebbian rules stabilize synchrony. Well-established metrics enable comprehensive characterization of chimera state dynamics in adaptive neural networks, providing detailed quantitative insights into how temporal delays and synaptic plasticity govern collective neural behavior through systematic parameter exploration. While building upon established frameworks, our systematic analysis reveals specific parameter dependencies that enhance understanding of synchronization control mechanisms in layered neural systems.

This study creates and analyses a Leslie–Gower prey–predator scheme which includes the fear phenomenon and how it affects prey reproduction over time and space. The prey population experiences growth suppression arising from both direct predation and predator-induced fear, the latter of which persists even in the absence of direct encounters. The predator dynamics are governed by a Leslie–Gower framework, wherein the carrying capacity is determined by the availability of prey as the primary food resource. Diffusion terms are incorporated for both prey and predator populations to represent their spatial movement and dispersal. This formulation enables the investigation of spatial heterogeneity and the emergence of ecological pattern formations within the system. We explore the presence and stability of equilibria, the circumstances under which predators and prey can coexist, and examine the impact of fear and its lingering effects on long-term dynamics. Furthermore, the study explores the influence of diffusion on spatial stability, diffusion-driven (Turing) instabilities, and the associated dispersion relations with respect to the wave number, particularly under the combined effects of fear and its carry-over effects (COE). Numerical simulations are conducted to enhance the analytical findings, revealing a diverse range of spatio-temporal dynamics, including predator extinction, stable coexistence, and the formation of spatial structures. The results underscore the critical ecological significance of fear and its persistent carry-over effects in shaping population stability and spatial organization.

This paper investigates a class of malignant tumor spread models that balance the concentrations of invasive cells and the extracellular matrix. Using symmetry methods, invariant solutions are derived for the reaction-diffusion system governing tumor invasion. For a particular solution, numerical analysis reveals oscillatory spatial behavior governed by two parameters, with exponential growth in invasive cell concentration and linear growth in matrix degradation, which is characteristic of malignant tumors. New global existence results for classical solutions are established using fixed point theorems for the sum of two operators, proving the existence of one or more nonnegative solutions under suitable conditions. The approach combines the Kuratowski measure of noncompactness with expansive operator theory. A concrete mathematical example illustrates that the assumptions and conditions of the results can be satisfied.