Introduction: This paper introduces the notion of controlled ultrametric type spaces, a new generalization designed to deepen and broaden the analytical structure of ultrametric frameworks. The study examines the fundamental properties of these spaces, provides illustrative examples, and positions them as a versatile setting for fixed-point analysis. Methods: Within this newly defined framework, we establish Banachtype, Fisher-type, and Kannan-type contractive principles. Each theorem is supported by rigorous proofs that highlight the central role of the control function in shaping the behaviour of the underlying space. The approach is structured to demonstrate how controlled ultrametric type spaces offer stronger and more flexible tools than their classical counterparts. Results: Several fixed-point theorems are derived under the proposed contractive conditions. These results demonstrate how the control function affects convergence dynamics and the existence of fixed points. Examples are included to validate the theoretical developments and illustrate their operational effectiveness. Conclusion: The generalisation proposed in this work expands the scope of fixed point theory in ultrametric-type environments and provides analytical advantages for future research in functional equations, topology, and nonlinear analysis. Moreover, a practical application to radar range correction is presented, demonstrating the potential of controlled ultrametric type spaces in real-world modelling and computational tasks.
Introduction/purpose: Inland ports provide storage, transportation, and customs clearance services for goods moving within inland areas. Ranking and evaluating inland ports are crucial to national logistics, thereby improving management efficiency and optimizing the flow of goods. The current study demonstrates a capacity-focused capability assessment of eight inland ports in Vietnam. Methods: The comparison is made based on four main parameters: throughput capacity, total area, warehouse area, and maximum exploitation output. Three multi-criteria modelling (MCM) methods, including the Probability Method (PM), objective pairwise adjusted ratio analysis (OPARA), and Root Assessment Method (RAM), were applied to rank the inland ports. The LOPCOW (Logarithmic Percentage Change-driven Objective Weighting) method is used to determine the criteria weights. Rankings from individual methods are aggregated using the Rank Index method (RIM). Results: The results show that, regardless of the method employed or the criterion weights used, one inland port (A2) performs best among the eight surveyed ports. To assess the stability of the outcome, five scenarios are generated, varying the criterion weights and the ranking of alternatives in each case. The result shows that the outcome is less sensitive to the changes in external conditions. Conclusion: This study provides transport companies with information to select the optimal inland port based on throughput capacity and warehouse area, supports exporters and importers in optimizing storage and transportation processes, provides the government with data to enhance management, and guides other ports in improving their operating capacity.
Background/Aim: This study aims to investigate the impact of a hydrogen-rich environment on the mechanical properties of an Al-Mg-Si aluminum alloy from the 6xxx series. Such alloys can exhibit hydrogen embrittlement (HE), especially in aqueous environments. The extent of this embrittlement depends on various microstructural parameters and any heat treatments that the alloy has undergone. Methods: Experimental work was conducted on cylindrical test specimens that underwent a homogenisation cycle involving rapid cooling by super-saturation in water (SSW), followed by natural cooling to ambient temperature. This was followed by artificial ageing (AA) tempering after cooling in open air. The samples were pre-charged using the cathodic charging method for different periods ranging from two to eight hours in a simulated environment of 0.05 M sulfuric acid (H₂SO₄) at a current density of 70 mA/cm². Results: The results, presented in the form of experimental curves recorded after a mechanical tensile fracture test, consist of breaking the loaded test pieces at ambient temperature. The mechanical characteristics were analysed by hardness tests before and after loading. Scanning electron microscopy reveals the presence of ODA inclusions, which are non-metallic impurities that act as preferred sites for crack initiation. This confirms the mechanism of hydrogen embrittlement, resulting in a decrease in elongation at break. Conclusion: There was a noticeable decline in mechanical performance, especially in yield strength and elongation at fracture, during hydrogen charging. The alloy's sensitivity to hydrogen was confirmed by the fact that the level of absorbed hydrogen rose with charging time. An embrittlement index (EI%) was used to measure the hydrogen-induced loss of ductility, reaching 30%.
Background/aim: Paint components can contain various organic and inorganic substances that are harmful to human health and the environment. This can also be the case for ammunition paints. Therefore, improperly stored or abandoned ammunition can become a source of contamination. Methods: The presence of heavy metals, asbestos, polychlorinated biphenyls (PCB) and chlorinated paraffins was investigated in ammunition objects from different time periods. Results: No asbestos and only little chlorinated paraffins were found. 2 of 21 samples contained elevated PCB-concentrations >150 mg/kg. Most prominent metals found were Pb, Cr, Zn, Ba and Ti, reaching values of over 89 g/kg, 25 g/kg, 230 g/kg, 87 g/kg and 190 g/kg, respectively. The presence of PCBs and heavy metals can be historically explained with their prevalence in the paint industry and correlated to bans and the use of alternative products. Some concentrations were found to be high enough to raise concerns in terms of health effects and restrictions for disposal. Example calculations were done to evaluate the role of contaminants originating from paints. For this purpose, an actual ongoing ordnance remediation project in Switzerland was used and calculations were made for Pb, Zn, Ba and Cr. For these four elements, potential contamination proportions originating from paint were estimated to account for 0.06%, 0.4%, 40% and even 100%, respectively. Conclusion: Paint contaminants can play an important role in the overall material budget and should be accounted for during future ordnance-caused remediation projects.
Background/Aim: This paper addresses the challenge of bounding zeros of quaternionic polynomials, a problem with applications in control theory and quantum mechanics, by developing new techniques that improve upon classical Frobenius-norm methods. Methods: We derive new upper bounds by analyzing the spectral and numerical radii of companion matrices. Our approach integrates Aluthge transforms and partitioned matrix analysis within the quaternionic framework. Results: The main results are explicit, computationally efficient formulas for zero bounds that are proven to be sharper than existing methods. The improvement is demonstrated through numerical examples and comparative analysis. Conclusions: The presented methods provide tighter bounds for quaternionic polynomial zeros, advancing quaternionic linear algebra and offering practical tools for the stability analysis of quaternionic systems.
Background/Aim: Multilayered piezoelectric energy harvesters suffer from a critical trade-off between mechanical reliability and electrical performance due to internal stress states. This study establishes an analytical framework to optimize the piezoelectric layer thickness (h₂) for simultaneously minimizing stress concentrations and maximizing harvested power in semiconductor-based structures. Methods: A fully coupled electromechanical model is formulated, integrating material gradation, thermo-piezoelectric coupling, and a thickness-dependent efficiency parameter. The constitutive equations are solved via a modified Rayleigh-Ritz method, yielding closed-form analytical expressions for mechanical stress, surface charge density, and energy conversion efficiency. Results: Within the optimal thickness range of 0.03-0.05 mm, the conventional trade-off between mechanical reliability and electrical performance is overcome. A critical thickness suppresses tensile stress nucleation while delivering a peak power density of 1.20 µW/cm², significantly outperforming non-optimized architectures. Conclusion: This research provides a quantitative, physics-based design methodology for tailoring multilayered energy harvesters with enhanced durability and efficiency. The framework enables predictive material and geometric selection, advancing the scalability and reliability of autonomous micro-power systems for wearable electronics, IoT sensors, and biomedical devices.
Introduction/Objective: On the modern battlefield, a soldier's combat readiness is directly dependent on the proper use of specific military equipment (SME). Automatic verification of SME usage, primarily ballistic helmets and combat vests, is a critical factor for risk reduction and increasing combat effectiveness. Traditional object detection (bounding box) is inadequate for military conditions due to camouflage and occlusion. The objective of this paper is the development, rigorous optimization, and validation of an efficient system for real-time SME segmentation, based on a modern, lightweight YOLO12-seg architecture. Methods: The system was trained on a custom-created "Mil-SME-Seg" dataset focused on military personnel. An advanced set of data augmentations (Mosaic, MixUp, HSV-shift) was applied to achieve robustness. A systematic optimization of the key "number of epochs" hyperparameter was performed through five independent, repeatable training runs (100, 120, 150, 200, and 250 epochs) to identify the optimal balance between accuracy and overfitting. Performance was evaluated using a comprehensive set of segmentation metrics, including mAP50-95(M), mAP50(M), mAP75(M), and F1-Score(M). Results: Experiments showed that training for 150 epochs yields the best generalized results on the validation set. Peak performance was achieved at epoch 144, with an mAP50-95(M) of 0.6128, mAP50(M) of 0.7852, and an F1-Score(M) of 0.741. Metric analysis indicates that longer training runs (200 and 250 epochs) lead to clear performance degradation due to overfitting. Qualitative analysis confirms the superiority of segmentation in tactically relevant scenarios (camouflage, partial occlusion). Conclusion: The optimal number of epochs for training the model on this dataset is approximately 150. The resulting model, integrated into a system with support for dynamic "military scenarios," proved its practical applicability and tactical value, achieving real-time processing speeds (48-55 FPS). This paper lays the foundation for future systems that will use segmentation masks for equipment damage assessment and sensor fusion.
Introduction/purpose: Underground mining environments contain numerous electromagnetic sources whose cumulative emissions may increase occupational exposure to non-ionizing radiation (NIR). The aim of this study is to assess exposure levels and propose a management model for NIR control in a mining technical room. Methods: Field measurements of electric and magnetic fields were conducted using a Narda NBM-550 system, combined with three-dimensional electromagnetic simulations performed in CST Studio Suite. Measurements and simulations were carried out in three critical mining zones: Main Transport Tunnel, Technical Room, and Power Supply Area. Results: The highest electric field level was recorded in the Technical Room due to simultaneous operation of multiple wireless and electrical sources. Simulation results confirmed field superposition and reflection effects, with local peak values reaching 25.2 V/m (41% of ICNIRP reference limits). Conclusion: The integration of measurements and simulations enables a holistic management approach for occupational NIR exposure. The proposed model supports risk assessment, preventive planning, and continuous monitoring in complex underground environments.
Introduction/purpose: This research investigates the durability of roller-compacted concrete pavement (RCCP) incorporating reclaimed asphalt pavement (RAP) as a partial or full replacement for natural aggregates (NA). The primary objective is to assess the feasibility of using RAP in pavement concrete from both performance and sustainability perspectives. ACKNOWLEDGMENT: This research was supported by the Innovative Materials Laboratory and Renewable Energies, Civil Engineering Department, University of Relizane, Algeria, under the authority of the Ministry of Higher Education and Scientific Research. Methods: Concrete mixtures were prepared with four RAP substitution levels: 25%, 50%, 75%, and 100%. Durability tests were performed to evaluate the resistance of these mixes to acid and sulfate attacks. Additionally, microstructural analyses were conducted using scanning electron microscopy (SEM) and X-ray diffraction (XRD) to examine internal changes resulting from chemical exposure. Results: The incorporation of RAP improved durability against acid and sulfate attacks, particularly at substitution levels up to 50%. Beyond this threshold, a slight decline in performance was observed, though it remained within acceptable limits. SEM images revealed a denser matrix and stronger bonding between the cement paste and RAP aggregates. XRD analysis confirmed the presence of stable hydration products, even after exposure to aggressive solutions. Conclusion: The findings support the use of RAP as a viable and sustainable alternative to NA in RCCP. At optimal substitution levels, it enhances durability, contributes to environmental protection, reduces construction waste, and offers cost-effective solutions by utilizing recycled materials.
Introduction/purpose: The purpose of this research is to determine the priority of Key Performance Indicators (KPIs) in a precise and structured manner. By applying the fuzzy multi-attribute decision-making model, operational management can identify and prioritize activities that will enhance maintenance process reliability in the shortest possible time while simultaneously reducing costs. Methods: The relative importance of sub-processes and KPI values is represented using predefined linguistic terms modelled by interval type-2 fuzzy numbers (IT2FNs). These assessments are formulated as a fuzzy group decision-making framework. The weight vector is determined using the fuzzy geometric mean, while the ranking of KPIs is obtained through the Taxonomy method combined with IT2FNs, which represents the main scientific contribution of this research. Results: Real-world data gathered from a maintenance depot were used to test the proposed model. The study effectively modelled uncertainty in KPI evaluations using seven predefined linguistic expressions mapped onto IT2FNs. A consistent weight vector was obtained using the fuzzy group decision-making approach. Effective KPI ranking was achieved through a combination of the Taxonomy method and IT2FNs, which helped pinpoint the most important areas for operational improvement. The method's ability to provide clear priorities to support reliability improvements while cutting costs was validated through its application. Conclusion: The key contributions of this study are: (i) fuzzy algebra rules with IT2FNs are used to determine the group utility value, and (ii) the integration of the Taxonomy method with IT2FNs for an improved decision-making procedure.
Introduction/purpose: This study aims to valorize a local material from the western region of Algeria for potential use in road construction. The main objective is to investigate the effect of incorporating synthetic polypropylene fibers and natural Alfa plant fibers at varying contents (0%, 0.3%, 0.6%, and 0.9%) on the strength of a silty sand stabilized with 4% cement. Methods: An experimental program was conducted using unconfined compression tests and unconsolidated-undrained triaxial tests. These tests were performed on soil-fiber-cement mixtures compacted statically at the Standard Optimum Proctor (SOP) conditions (γ dmax= 17 kN/m3 and wopt =16.6%) and cured for 1, 7, and 28 days in open air. Results: The results revealed a significant improvement in the mechanical strength of the treated soil, with a change in the failure behavior from brittle to ductile. The addition of 0.3% fibers enhanced cohesion while reducing the internal friction angle. Furthermore, fiber-reinforced cemented samples exhibited greater stiffness compared to untreated soil. Moreover, the highest unconfined compressive strength was obtained with the combination of 0.9% fiber reinforcement and 4% cement. Conclusion: The reinforcement of cemented silty sand with polypropylene and Alfa fibers significantly improves its mechanical strength and stiffness. The addition of 0.9% fiber content yields the highest compressive strength while effectively transitioning the soil's behavior from brittle to ductile. These findings confirm that valorizing local Algerian materials is a technically viable and sustainable solution for road infrastructure development.
Introduction/purpose: This work studies natural convection within a porous cavity with undulated vertical walls focusing on investigating the effects of various heating scenarios. The model consists of a square cavity with sinusoidal undulations on its vertical walls. The cavity is characterized by a square cross-section, and the undulations are described by a sinusoidal wave function with a specific amplitude and wavelength. The left vertical wall of the cavity is maintained at a constant cold temperature, while the bottom wall is subjected to various heating profiles, including linear heating, constant heating, parabolic heating, and sinusoidal heating. The choice of these different heating scenarios is intended to explore how the heat transfer behavior changes under each condition. The top and right walls are assumed to be adiabatic. Methods: The effects of heating methods and Darcy number on fluid flow and heat transfer in the cavity under a high Rayleigh number are numerically analyzed. Results: Results show that all heating profiles create distinct thermal gradients, influencing the vortex strength and flow complexity. The study also investigates the irreversibilities within the system, focusing on entropy generation due to both heat transfer and fluid friction, to evaluate the thermodynamic efficiency of the cavity. Conclusion: The study aims to provide a comprehensive understanding of how heating conditions, permeability variations and high Rayleigh number convection affect the thermal and fluid dynamics in porous cavities, with implications for improving the performance of thermal management systems in practical engineering applications.
Introduction/purpose: The study aims to model fatigue-related crack propagation by introducing a numerical method, CPCN-FEM (Crack Propagation by Coordinates of Nodes - Finite Element Method), which predicts crack trajectories through the systematic generation of nodal coordinates around the crack front. Methods: The approach defines four principal nodes to control the propagation direction and computes the stress intensity factors (K I) and (KII), along with the crack inclination angle (β). The method was implemented in FORTRAN to automate node tracking, coordinate updating, and stepwise crack advance in a two-dimensional elastic isotropic model. Simulations were conducted and compared with analytical crack-path solutions, using the Richard criterion to determine crack orientation. Results: The numerical model reproduced expected crack trajectories with high agreement with analytical predictions and demonstrated stable displacement behavior across multiple propagation cases. Mesh integrity was preserved during all propagation steps, and no remeshing was required. Conclusion: The findings show that CPCN-FEM provides an accurate, efficient, and mesh-preserving technique for modeling crack growth under fatigue, offering reliable predictions of crack path evolution in fracture mechanics.
Introduction/purpose: Urban traffic crossroads represent highly complex nodes within transportation networks due to the convergence of multiple, often conflicting, traffic streams. Managing these competing flows poses significant challenges, leading to issues such as fluctuating delays and backflow, particularly at supersaturated intersections. Given that these crossroads frequently act as bottlenecks, accurate short-term traffic flow predictions are crucial for effective planning and congestion mitigation. This study aims to propose a robust, multi-criteria evaluation framework for crossroad design to support optimized urban planning and traffic management. Methods: To address the inherent complexities and uncertainties associated with evaluating such designs, this research employs the Fuzzy Analytic Hierarchy Process (FAHP). This method is particularly suited for contexts in which expert judgments, often involving qualitative criteria such as landscape integration and local economic impact, lack absolute precision. Our approach integrates fuzzy logic to manage the subjective and imprecise nature of these evaluations, alongside quantitative factors such as cost and traffic saturation. Based on an extensive literature review and established disciplinary standards in traffic engineering and urban planning, we developed a comprehensive grid of 32 criteria and sub-criteria. These criteria cover key aspects such as road safety, service level, and traffic flow. Experts then assign weights to these criteria, which are processed through FAHP to produce a global performance indicator. This indicator allows the ranking and comparison of different alternative designs. Results: The application of this FAHP-based framework yields a global performance indicator that facilitates the objective ranking of alternative crossroad designs. The methodology provides a structured approach to balance multiple, often conflicting, criteria in complex decision environments. The practical relevance of this method is demonstrated through a case study of the Chettia junction, where it successfully identifies the optimal configuration among several proposed alternatives. This underscores FAHP's versatility in evaluating performance within intricate urban systems. Conclusion: This study successfully situates FAHP within a broader Multi-Criteria Decision Analysis (MCDA) framework, offering an original application to crossroad design. By integrating fuzzy logic, it effectively manages the uncertainty associated with both qualitative and quantitative evaluation criteria, proving particularly valuable when precise expert judgments are difficult for experts to provide. The proposed framework provides a robust and multidimensional evaluation tool for urban planners and traffic engineers, enabling more informed and optimized infrastructure decisions for complex urban intersections.
Introduction/purpose: Mineral and spring waters play a crucial role in daily nutrition due to their taste and health benefits. In Algeria, the bottled water market is rapidly growing, yet there remains a lack of precise, objective systems to classify these waters based on organoleptic qualities and safety. This study aims to develop a reliable numerical model for the hydrochemical classification of bottled waters marketed in Algeria. Methods: A hybrid multi-criteria decision-making approach was employed, integrating the DIBR II method to determine the weights of criteria based on expert judgments and the Bonferroni operator to aggregate these opinions. To effectively manage uncertainty and imprecision in the data, Triangular Neutrosophic Numbers (TNN) were utilized. Subsequently, the CODAS (COmbinative Distance-based ASsessment) method was applied to rank the bottled water brands. The evaluation focused on four key quality criteria: nitrate concentration, hardness, total mineralization, and hydrochemical nature. After constructing and aggregating the neutrosophic decision matrices and performing de-neutrosophication, CODAS computed a proximity coefficient for each brand, resulting in the final ranking. Results: The study identified the top five brands of mineral waters (Daouia, Mansourah, Youkous, Alma, and N'Gaous) and spring waters (Taya, Ariaf, Arwa, Sidi Rached, and Hirouche). Sensitivity analysis confirmed the robustness of the ranking, validating the model's reliability and showed that nitrate content is the most influential criterion, highlighting its key role in assessing water quality. Comparative analysis also demonstrated that CODAS produces consistent and reliable rankings compared to other multi-criteria methods, with good discrimination among closely ranked alternatives. Conclusion: This study developed an innovative and robust numerical model combining DIBR II and CODAS within a neutrosophic framework, providing a reliable hydrochemical classification of bottled mineral and spring waters in Algeria. The model incorporates expert weighting and accounts for data uncertainty to generate a clear and coherent brand ranking. Sensitivity analysis confirmed the stability of the rankings, particularly emphasizing the dominance of the nitrate criterion, demonstrating the model's value as a decision-support tool for various stakeholders in the sector.
Introduction/purpose: This research develops a systematic methodology for assessing the seismic vulnerability of buried water supply and wastewater pipeline networks. The objective is to integrate geological, geotechnical, and structural parameters within a unified decision-support framework, thus enabling infrastructure managers to identify and prioritize vulnerable segments in earthquake-prone regions. Methods: The methodology combines the Vulnerability Index (VI) approach with the Analytic Hierarchy Process (AHP) to assign relative weights to factors such as pipe material, diameter, age, burial depth, soil type, liquefaction potential, seismic intensity, and fault crossings. Expert judgment and pairwise comparisons are used to determine these weights. Geographic Information System (GIS) tools and field surveys support the spatial analysis. The approach is applied to the city of Blida, Algeria, characterized by high seismic hazard and diverse soil conditions. Results: The AHP-based VI approach produced detailed vulnerability maps for both water and sewer networks, classifying pipeline segments into low, medium, and high vulnerability levels. The method demonstrated higher precision and contextual relevance compared to empirical assessments, revealing material brittleness, diameter, and geotechnical conditions as key determinants. Conclusion: The AHP-VI framework provides a robust, adaptable, and transparent tool for seismic risk assessment of lifeline infrastructure. Its applicability extends to both civilian and military contexts, supporting strategic planning, targeted mitigation, and resilience enhancement of critical buried pipelines in seismically active regions.
Introduction/purpose: This study introduces a novel analytical framework to comprehensively investigate the natural vibration characteristics of porous functionally graded (FG) plates. The research aims to combine an innovative shape function methodology with a sophisticated porosity model within an advanced higher-order shear deformation theory (HSDT). Methods: Material properties follow power-law distributions across the thickness, with voids incorporated via a refined porosity formulation. The governing equations for simply supported plates are solved analytically using the Navier technique. A parametric study examines the effects of power-law index, geometric ratios, and porosity distribution. Results: Results show exceptional agreement with established theories, revealing significant relationships in which both the power-law index and porosity distribution critically influence natural frequencies. New insights are provided into their coupled effects on vibrational behavior. Conclusion: This work offers fundamental understanding for optimizing porous FG plate design in advanced engineering applications such as aerospace and structural systems, where weight reduction and vibration control are crucial. It delivers practical guidelines for engineering design and material selection.
Introduction/purpose: The noise generated by artillery firing can have an extremely harmful effect on the people using it, namely the crew. The subject of this paper is the measurement and analysis of noise levels on artillery weapons used in the Serbian Army. Methods: The analysis and comparison of the results were carried out during operation of weapons of different calibers. Also, the aspect of impact and risk on the crew exposed to the mentioned physical phenomena was considered. Results: The results of the examination of the acoustic parameters in relation to the available criteria show that the crew on certain vehicles is exposed to a higher level of noise than allowed. Conclusion: It is concluded that all measured noise levels exceed the prescribed limit value. Based on the obtained results, further work can be done on reducing negative physical phenomena, as well as providing adequate equipment for the protection of the crew.
Introduction/purpose: The paper proposes an electro-mechanical impact sensor for grenade detonation using an all-ways action mechanism with permanent magnets and a Hall sensor. After experimental validation, a mathematical model assesses how structural parameters, such as activation threshold, inertial mass, and Hall sensor placement, affect the fuse's sensitivity. The study provides recommendations for optimal sensor design to ensure reliable activation at all impact angles. Methods: The study used a combined approach to address the problem. Dynamic equations of the all-ways action mechanism were solved using the Runge-Kutta method, the magnetic field was simulated with FEMM 4.2 software, and the Hall voltage variation over time was analyzed to assess the fuse's sensitivity under grenade impact conditions. Results: The results show that an activation threshold below 80 mV ensures reliable operation at any impact angle with an impact velocity not greater than 2.5 m.s-1. The mass of the inertial object has a significant impact on the sensitivity, more than the mass of the magnet, and the location of the Hall sensor is critical, with some locations providing stable sensitivity and others resulting in poor performance. Conclusion: The hybrid method presented in this paper effectively studies the signal from an electro-mechanical impact sensor combining an all-ways action mechanism, permanent magnets, and a Hall sensor. The research results are useful contributions to the design of impact sensors in grenade fuses.
Introduction/purpose: The aim of this paper is to study the existence of mild solutions to the initial value problem (IVP for short) of the Darboux problem for partial hyperbolic fractional differential equations via the Caputo derivative with finite delay in Fréchet spaces. Methods: In our analysis, Darbo's fixed point theorem is employed together with the notion of measure of noncompactness to establish the existence of solutions by reducing the research to proving the existence and uniqueness of fixed points of appropriate operators. Results: Under suitable conditions, existence of mild solutions to the considered fractional partial hyperbolic differential equations is proved. An illustrative example demonstrates the theoretical results applicability. Conclusion: Throughout this paper, sufficient conditions were considered to establish the existence and uniqueness of solutions to the Darboux problem by applying Darbo's fixed point theorem on unbounded interval. The study provides a rigorous methodological framework for analyzing similar classes of problems and contributes to the broader understanding of mild solutions in fractional calculus and functional analysis. The results offer potential applications for researchers investigating fractional differential equations in infinite-dimensional spaces.
