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Keywords = RLC circuits

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18 pages, 7115 KB  
Article
Inductive Sensor Characteristics for Conductivity Measurement of Non-Ferromagnetic Metals Based on Single-Layer Solenoid
by Huan Wang, Ziyi Han, Yongjian Chen, Shuyu Li, Haoran Li, Hao Shen and Chunlong Xu
Sensors 2025, 25(17), 5566; https://doi.org/10.3390/s25175566 - 6 Sep 2025
Viewed by 974
Abstract
For the measurement of electrical conductivity of metal materials, the traditional contact measurement method has a limited test range and requires periodic electronic calibration. In order to overcome the above shortcomings, this paper takes the inductive response of an RLC circuit driven by [...] Read more.
For the measurement of electrical conductivity of metal materials, the traditional contact measurement method has a limited test range and requires periodic electronic calibration. In order to overcome the above shortcomings, this paper takes the inductive response of an RLC circuit driven by alternating sources as the research object and proposes a non-contact method for conductivity measurement of non-ferromagnetic metals engaged by a single-layer solenoid sensor. The effect of the circuit parameters on the inductive sensor characteristics has been described with different resonant modes, and the electric conductivities of different metals can be theoretically calculated based on eddy current. Moreover, the Comsol Multiphysics software is used to conduct finite element analysis to compare the experimental results and the simulation, which is consistent with the theoretical analysis. The measured accuracy of the inductive sensor is verified to be higher than 91% in parallel resonance, which exhibits higher stability and precision than that of series mode. The implementation of this project will provide the theoretical basis and data reference for the detection of electromagnetic properties of unknown metals and has a wide range of applications in non-destructive testing, engineering construction detection, and other fields. Full article
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38 pages, 11916 KB  
Article
Compressing Magnetic Fields by the Electromagnetic Implosion of a Hollow Lithium Cylinder: Experimental Test Beds Simulated with OpenFOAM
by Victoria Suponitsky, Ivan V. Khalzov, David M. Roberts and Piotr W. Forysinski
Fluids 2025, 10(9), 222; https://doi.org/10.3390/fluids10090222 - 25 Aug 2025
Viewed by 603
Abstract
Electromagnetic implosions of hollow lithium cylinders can be utilized to compress magnetized plasma targets in the context of Magnetized Target Fusion (MTF). Two small-scale experiments were conducted at General Fusion as a stepping stone toward compressing magnetized plasmas on a larger scale. The [...] Read more.
Electromagnetic implosions of hollow lithium cylinders can be utilized to compress magnetized plasma targets in the context of Magnetized Target Fusion (MTF). Two small-scale experiments were conducted at General Fusion as a stepping stone toward compressing magnetized plasmas on a larger scale. The first experiment is an electromagnetic implosion of a lithium ring, and the second is a compression of toroidal magnetic flux by imploding a hollow lithium cylinder onto an hourglass-shaped central structure. Here we present the methodology and results of modelling these experiments with OpenFOAM. Our in-house axisymmetric compressible MHD multi-phase solver was further extended to incorporate: (i) external RLC circuit model for electromagnetic compression coils and (ii) diffusion of the magnetic field into multiple solid materials. The implementation of the external RLC circuit model for electromagnetic coils was verified by comparison with results obtained with FEMM software and with the analytical solution. The solver was then applied to model both experiments and the main conclusions are as follows: (i) modelling solid lithium as a high-viscosity liquid is an adequate approach for the problems considered; (ii) the magnetic diffusivity of lithium is an important parameter for the accurate prediction of implosion trajectories (for the implosion of the lithium ring, higher values of magnetic diffusivity in the range 0.2  ηring[m2/s]  0.5 resulted in a better fit to the experimental data with a relative deviation in the trajectory of 20%); (iii) simulation results agree well with experimental data, and in particular, the toroidal field amplification of 2.25 observed in the experiment is reproduced in simulations within a relative error margin of 20%. The solver is proven to be robust and has the potential to be employed in a variety of applications. Full article
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13 pages, 3394 KB  
Article
Design of a Wideband Loaded Sleeve Monopole Embedded with Filtering High–Low Impedance Structure
by Jiansen Ma, Weiping Cao and Xinhua Yu
Electronics 2025, 14(15), 3137; https://doi.org/10.3390/electronics14153137 - 6 Aug 2025
Viewed by 407
Abstract
In this paper, a compact wideband filtering monopole is presented for remote terrestrial omnidirectional communication systems. The presented antenna features a sleeve monopole structure integrating with two key components: the lumped parallel RLC circuits and an embedded high–low impedance structure within the sleeve [...] Read more.
In this paper, a compact wideband filtering monopole is presented for remote terrestrial omnidirectional communication systems. The presented antenna features a sleeve monopole structure integrating with two key components: the lumped parallel RLC circuits and an embedded high–low impedance structure within the sleeve section. The integrated high–low impedance structure enables the monopole to achieve excellent filtering characteristics while maintaining the monopole compactly. Meanwhile, the combination of the RLC loads and the sleeve monopole ensures wideband omnidirectional radiation performance. To validate the design, a prototype operating from 200 to 1500 MHz is fabricated and tested. The measurement results demonstrate that the monopole achieves a VSWR below 3 across the entire operating band and a measured gain exceeding 0 dB. Furthermore, the monopole exhibits satisfactory out-of-band rejection from 1700 to 4000 MHz, confirming its effective filtering capability. Full article
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21 pages, 3892 KB  
Article
Quantitative Analysis of the Fault Ride-Through Current and Control Parameters in Hybrid Modular Multilevel Converters
by Yi Xu and Bowen Tang
Appl. Sci. 2025, 15(15), 8331; https://doi.org/10.3390/app15158331 - 26 Jul 2025
Viewed by 376
Abstract
A quantitative analysis of the fault transient is critical for system resilience assessment and protection coordination. Focusing on hybrid modular multilevel converter (MMC)-based HVDC architecture with enhanced fault ride-through (FRT) capability, this study develops a mathematical calculation framework to quantify how controller configurations [...] Read more.
A quantitative analysis of the fault transient is critical for system resilience assessment and protection coordination. Focusing on hybrid modular multilevel converter (MMC)-based HVDC architecture with enhanced fault ride-through (FRT) capability, this study develops a mathematical calculation framework to quantify how controller configurations influence fault current profiles. Unlike conventional static topologies (e.g., RLC or fixed-voltage RL circuits), the proposed model integrates an RL network with a time-variant controlled voltage source, which can emulate closed-loop control response during the FRT transient. Then, the quantitative relationship is established to map the parameters of DC controllers to the fault current across diverse FRT strategies, including scenarios where control saturation dominates the transient response. Simulation studies conducted on a two-terminal MMC-HVDC architecture substantiate the efficacy and precision of the developed methodology. The proposed method enables the evaluation of DC fault behavior for hybrid MMCs, concurrently appraising FRT control strategies. Full article
(This article belongs to the Special Issue Power Electronics: Control and Applications)
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24 pages, 11109 KB  
Review
Review of Self-Powered Wireless Sensors by Triboelectric Breakdown Discharge
by Shuzhe Liu, Jixin Yi, Guyu Jiang, Jiaxun Hou, Yin Yang, Guangli Li, Xuhui Sun and Zhen Wen
Micromachines 2025, 16(7), 765; https://doi.org/10.3390/mi16070765 - 29 Jun 2025
Viewed by 1112
Abstract
This review systematically examines recent advances in self-powered wireless sensing technologies based on triboelectric nanogenerators (TENGs), focusing on innovative methods that leverage breakdown discharge effects to achieve high-precision and long-distance signal transmission. These methods offer novel technical pathways and theoretical frameworks for next-generation [...] Read more.
This review systematically examines recent advances in self-powered wireless sensing technologies based on triboelectric nanogenerators (TENGs), focusing on innovative methods that leverage breakdown discharge effects to achieve high-precision and long-distance signal transmission. These methods offer novel technical pathways and theoretical frameworks for next-generation wireless sensing systems. To address the core limitations of conventional wireless sensors, such as a restricted transmission range, high power consumption, and suboptimal integration, this analysis elucidates the mechanism of the generation of high-frequency electromagnetic waves through localized electric field ionization induced by breakdown discharge. Key research directions are synthesized to enhance TENG-based sensing capabilities, including novel device architectures, the optimization of RLC circuit models, the integration of machine learning algorithms, and power management strategies. While current breakdown discharge sensors face challenges such as energy dissipation, multimodal coupling complexity, and signal interpretation barriers, future breakthroughs in material engineering and structural design are anticipated to drive advancements in efficiency, miniaturization, and intelligent functionality in this field. Full article
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25 pages, 11913 KB  
Article
Research on the Remanence Measurement Method of Transformers Based on the Degaussing Hysteresis Loop
by Dingyuan Li, Jing Zhou, Zhanlong Zhang, Yu Yang, Zijian Dong, Wenhao He, Xichen Pei, Jiatai Gao, Siyang Chen and Zhicheng Pan
Appl. Sci. 2025, 15(10), 5375; https://doi.org/10.3390/app15105375 - 12 May 2025
Viewed by 527
Abstract
The residual magnetism of the iron core of power transformers can cause an excitation inrush current, posing a threat to the safe and stable operation of the power grid. This paper proposes a transformer remanence measurement method based on a demagnetization hysteresis loop [...] Read more.
The residual magnetism of the iron core of power transformers can cause an excitation inrush current, posing a threat to the safe and stable operation of the power grid. This paper proposes a transformer remanence measurement method based on a demagnetization hysteresis loop to address the problems of large errors, complex operation, and poor universality in existing remanence measurement methods. This method is designed for off-grid transformers to avoid potential interference to the power grid caused by current pulses during the measurement process. This method constructs an RLC oscillation circuit that utilizes capacitor energy storage and iron core magnetic field energy conversion, combined with the dynamic characteristics of hysteresis loops, to achieve accurate measurement of residual magnetism and synchronous demagnetization. The effectiveness of this method has been verified through residual magnetism measurement experiments on ring transformers and large converter transformers, and it can be applied in specific engineering practice operations. Theoretical analysis shows that the charging range of energy storage capacitors is affected by the hysteresis characteristics of the iron core and the saturation magnetic flux, and the residual magnetization value can be directly calculated based on the difference in the intersection point of the longitudinal axis of the demagnetization hysteresis loop. Simulation and experimental results show that the measurement error of the proposed method is less than 5%—significantly better than traditional methods. This method does not require complex control strategies, has high precision and efficiency, and can provide reliable technical support for residual magnetism detection and suppression of off-grid power transformers. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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22 pages, 677 KB  
Article
The LDG Finite-Element Method for Multi-Order FDEs: Applications to Circuit Equations
by Mohammad Izadi, Hari Mohan Srivastava and Mahdi Kamandar
Fractal Fract. 2025, 9(4), 230; https://doi.org/10.3390/fractalfract9040230 - 5 Apr 2025
Viewed by 571
Abstract
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the [...] Read more.
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article
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20 pages, 37593 KB  
Article
A Second-Order Fast Discharge Circuit for Transient Electromagnetic Transmitter
by Chao Tan, Shibin Yuan, Linshan Yu, Yaohui Chen and Changjiang He
Sensors 2025, 25(7), 2224; https://doi.org/10.3390/s25072224 - 1 Apr 2025
Cited by 1 | Viewed by 623
Abstract
To solve the problem of long turn-off times for transient electromagnetic (TEM) transmitters with inductive loads, a new second-order fast discharge circuit topology added into the original H-bridge structure for TEM transmitters is presented, which includes a capacitor, two Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs), [...] Read more.
To solve the problem of long turn-off times for transient electromagnetic (TEM) transmitters with inductive loads, a new second-order fast discharge circuit topology added into the original H-bridge structure for TEM transmitters is presented, which includes a capacitor, two Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs), and two resistors. Firstly, the four operating stages and principles of the second-order circuit were analyzed. Then, the mathematical models of the turn-off time of the current and the voltage stress of the Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) were established using the analytical method. Finally, the parameters of the resistor and capacitor were selected by finding the optimal solution for the fixed transmitter coil. Compared with the simulation results of the other two topologies, the proposed topology demonstrates a current-independent turn-off time and achieves the shortest duration at 50 A, while maintaining lower voltage stress at 9 A. The experimental results of the prototype show that the turn-off time is always about 64 μs when the currents are 1 A, 5 A, and 9 A. Simulation and experimental results show that the second-order circuit reduces the MOSFET’s turn-off time to 58 μs via Resistor–Inductor–Capacitor (RLC) series resonance, with the turn-off duration remaining load-current-independent. Full article
(This article belongs to the Special Issue Advanced Sensing and Control Technologies in Power Electronics)
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11 pages, 2833 KB  
Communication
Terahertz Metamaterial Absorber and Equivalent Circuit Model for Refractive Index Sensing
by Zhengxiong Lu, Peixuan Li, Chuanwei Zhang, Shuaitian Li, Ruibo Chen, Ziliang Zhou and Xiaojun Huang
Materials 2025, 18(4), 765; https://doi.org/10.3390/ma18040765 - 10 Feb 2025
Viewed by 1459
Abstract
As a kind of important functional device, terahertz metamaterial absorbers (TMA) have been focused on by many researchers for their capacity to absorb electromagnetic waves and wide application fields. In this work, we designed a terahertz metamaterial absorber with narrow-band absorption for refractive [...] Read more.
As a kind of important functional device, terahertz metamaterial absorbers (TMA) have been focused on by many researchers for their capacity to absorb electromagnetic waves and wide application fields. In this work, we designed a terahertz metamaterial absorber with narrow-band absorption for refractive index sensing, which consisted of a circular metal ring resonator and a square metal ring resonator. The simulation results show that the absorptivity of the proposed TMA reached over 68.8% and 93.27% at 1.926 and 4.413 THz, respectively. Moreover, the absorption mechanism was studied through the electromagnetic field energy distribution, and the influence of structural parameters on absorption performance was exhibited. In refractive index sensing, a high sensitivity (S) of 2.537 THz/RIU (refractive index unit, RIU) was achieved by utilizing the coupling of ring resonators. The maximal quality factor (Q-factor) and figure of merit (FOM) of the TMA were 234.73 and 147.67 RIU−1, respectively. Additionally, we established an RLC equivalent circuit model (ECM) for the TMA, and we further illustrated the performance of the TMA in refractive index sensing through fitting the sensitivity based on the ECM to the sensitivity of the TMA. Our study exhibits the considerable potential application for the field of terahertz sensing, and the ECM for refractive index sensing will be helpful for continual investigation. Full article
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22 pages, 579 KB  
Article
Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line
by Krzysztof Pomorski, Łukasz Pluszyński and Eryk Hałubek
Condens. Matter 2024, 9(4), 35; https://doi.org/10.3390/condmat9040035 - 26 Sep 2024
Viewed by 1840
Abstract
The model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other [...] Read more.
The model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other classes of potential. The analytical and numerical validation of Kron’s second model is conducted for different shapes of particle-confining potentials in the one-dimensional case using an LTspice simulator. Thus, there remains potential for obtaining solutions in two- and three-dimensional cases. Here, a circuit model representing a linearized Ginzburg–Landau equation is given. Kron’s second model is generalized by the introduction of linear and non-linear resistive elements. This transforms the deformed Schrödinger equation into a linear dissipative Schrödinger equation and its non-linear form. The quantum mechanical roton problem is the main result of this work and is formulated by means of classical physical states naturally present in the LC classical circular electrical transmission line. The experimental verification of Kron’s model is confirmed. Full article
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19 pages, 15534 KB  
Article
Research on Gate Charge Degradation of Multi-Chip IGBT Modules in Power Supply for Unmanned Aerial Vehicles
by Yuheng Li, Zhiquan Zhou, Jinlong Wang, Lina Wang and Chenxu Wang
Electronics 2024, 13(18), 3664; https://doi.org/10.3390/electronics13183664 - 14 Sep 2024
Viewed by 1122
Abstract
In recent years, with the burgeoning application of high voltage in various industrial sectors, the deployment of unmanned equipment, such as industrial heavy-load Unmanned Aerial Vehicles (UAVs), incorporating high-capacity Insulated-Gate Bipolar Transistors (IGBTs), has become increasingly prevalent. The demand for high-voltage IGBT modules [...] Read more.
In recent years, with the burgeoning application of high voltage in various industrial sectors, the deployment of unmanned equipment, such as industrial heavy-load Unmanned Aerial Vehicles (UAVs), incorporating high-capacity Insulated-Gate Bipolar Transistors (IGBTs), has become increasingly prevalent. The demand for high-voltage IGBT modules in UAV is continuously growing; therefore, exploring methods to predict fault precursor parameters of multi-chip IGBT modules is crucial for the operational health management of unmanned equipment like UAVs. This paper analyzes the gate charge degradation in multi-chip IGBT modules after thermal cycling, which can be used to evaluate the operational state of these modules. Furthermore, to delve into the electrical response of a gate drive circuit caused by local damage within the IGBT module, an RLC model incorporating parasitic parameters of the gate drive circuit is established, and a sensitivity analysis of the peak current in the gate charge circuit is provided. Additionally, in the experimental circuit, an open sample of an IGBT module with partial bond wires lifted off is used to simulate actual faults. The analysis and experimental results indicate that the peak current of the gate charge is closely related to L and C. The significant deviation in the gate current, influenced by the partial bond wires lift-off, can provide a basis for the development of predictive methods for IGBT modules. Full article
(This article belongs to the Section Industrial Electronics)
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21 pages, 1100 KB  
Article
Consensus of T-S Fuzzy Fractional-Order, Singular Perturbation, Multi-Agent Systems
by Xiyi Wang, Xuefeng Zhang, Witold Pedrycz, Shuang-Hua Yang and Driss Boutat
Fractal Fract. 2024, 8(9), 523; https://doi.org/10.3390/fractalfract8090523 - 5 Sep 2024
Cited by 17 | Viewed by 1302
Abstract
Due to system complexity, research on fuzzy fractional-order, singular perturbation, multi-agent systems (FOSPMASs) remains limited in control theory. This article focuses on the leader-following consensus of fuzzy FOSPMASs with orders in the range of 0, 2. By employing the T-S [...] Read more.
Due to system complexity, research on fuzzy fractional-order, singular perturbation, multi-agent systems (FOSPMASs) remains limited in control theory. This article focuses on the leader-following consensus of fuzzy FOSPMASs with orders in the range of 0, 2. By employing the T-S fuzzy modeling approach, a fuzzy FOSPMAS is constructed. In order to achieve the consensus of a FOSPMAS with multiple time-scale characteristics, a fuzzy observer-based controller is designed, and the error system corresponding to each agent is derived. Through a series of equivalent transformations, the error system is decomposed into fuzzy singular fractional-order systems (SFOSs). The consensus conditions of the fuzzy FOSPMASs are obtained based on linear matrix inequalities (LMIs) without an equality constraint. The theorems provide a way to tackle the uncertainty and nonlinearity in FOSPMASs with orders in the range of 0, 2. Finally, the effectiveness of the theorems is verified through an RLC circuit model and a numerical example. Full article
(This article belongs to the Section Engineering)
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21 pages, 4350 KB  
Article
Generalized Framework for Liquid Neural Network upon Sequential and Non-Sequential Tasks
by Prakash Kumar Karn, Iman Ardekani and Waleed H. Abdulla
Mathematics 2024, 12(16), 2525; https://doi.org/10.3390/math12162525 - 15 Aug 2024
Cited by 8 | Viewed by 7370
Abstract
This paper introduces a novel approach to neural networks: a Generalized Liquid Neural Network (GLNN) framework. This design excels at handling both sequential and non-sequential tasks. By leveraging the Runge Kutta DOPRI method, the GLNN enables dynamic simulation of complex systems across diverse [...] Read more.
This paper introduces a novel approach to neural networks: a Generalized Liquid Neural Network (GLNN) framework. This design excels at handling both sequential and non-sequential tasks. By leveraging the Runge Kutta DOPRI method, the GLNN enables dynamic simulation of complex systems across diverse fields. Our research demonstrates the framework’s capabilities through three key applications. In predicting damped sinusoidal trajectories, the Generalized LNN outperforms the neural ODE by approximately 46.03% and the conventional LNN by 57.88%. Modelling non-linear RLC circuits shows a 20% improvement in precision. Finally, in medical diagnosis through Optical Coherence Tomography (OCT) image analysis, our approach achieves an F1 score of 0.98, surpassing the classical LNN by 10%. These advancements signify a significant shift, opening new possibilities for neural networks in complex system modelling and healthcare diagnostics. This research advances the field by introducing a versatile and reliable neural network architecture. Full article
(This article belongs to the Special Issue Machine-Learning-Based Process and Analysis of Medical Images)
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17 pages, 499 KB  
Article
Analysis of Non-Local Integro-Differential Equations with Hadamard Fractional Derivatives: Existence, Uniqueness, and Stability in the Context of RLC Models
by Manigandan Murugesan, Saravanan Shanmugam, Mohamed Rhaima and Ragul Ravi
Fractal Fract. 2024, 8(7), 409; https://doi.org/10.3390/fractalfract8070409 - 12 Jul 2024
Cited by 3 | Viewed by 1681
Abstract
In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer’s fixed point theorem. To facilitate our key conclusions, [...] Read more.
In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer’s fixed point theorem. To facilitate our key conclusions, we convert the problem into an equivalent integro-differential equation. Additionally, we explore several versions of Ulam’s stability findings. Two numerical examples are provided to illustrate the applications of our main results. We also observe that modifications to the Hadamard fractional derivative lead to asymmetric outcomes. The study concludes with an applied example demonstrating the existence results derived from Schaefer’s fixed point theorem. These findings represent novel contributions to the literature on this topic, significantly advancing our understanding. Full article
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22 pages, 2754 KB  
Article
On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces
by Ekber Girgin, Abdurrahman Büyükkaya, Neslihan Kaplan Kuru and Mahpeyker Öztürk
Axioms 2024, 13(7), 441; https://doi.org/10.3390/axioms13070441 - 28 Jun 2024
Cited by 5 | Viewed by 1494
Abstract
In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed [...] Read more.
In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both 𝒵 simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit. Full article
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