International Journal of Dynamical Systems and Differential Equations (10 papers in press)

Regular Issues

• Fractional Calculus in Dynamic Analysis of Truck Frame: a Special Focus on Finite Element Modelling  
  by Yangyang Liu 
  Abstract: This paper investigates an innovative method to analyse and improve the dynamic performance of truck frames. Firstly, a 3D model of the frame was constructed by computer-aided design (CAD), and then meshing and material property sets were carried out by finite element analysis software to simulate the behaviour of the frame under variable working conditions. Fractional calculus is introduced to capture the nonlinear dynamic characteristics of the frame more accurately, and the Grunwald-Letnikov method is used to solve the relevant equations. Deep learning techniques extract key features from FEA data to identify stress concentration areas. Through dimensional optimisation experiments, this study also demonstrates how to adjust the frame plate thickness using gradient-based optimisation algorithms to achieve lightweight and performance improvement. Notably, the maximum stress value under bending conditions increases by 29.6 MPa, while under torsional conditions, it decreases by 65.7 MPa. This study highlights the synergistic potential of artificial intelligence, fractional calculus, finite element modelling, and deep learning techniques in advancing the dynamic analysis of truck frames, setting the stage for more resilient and efficient truck designs in the future.
  Keywords: Truck Frame; Artificial Intelligence; Fractional Calculus; Finite Element Analysis; Deep Learning Techniques; Dynamic Analysis.
  DOI: 10.1504/IJDSDE.2025.10068721
   
  
• A High-precision Broadband Low-Cost Multiplier Topology for Electric Energy Measurement  
  by Xiaoyan Yuan, Huafeng Cao, Kun Wang, Li Liang 
  Abstract: The multiplier is an indispensable component of electronic energy meters, and is also the main source of energy metering errors. This paper quantitatively analyses the metering error of the conventional time-division multiplier in the presence of harmonics. The theoretical error ex-pression is derived, which indicates that the error increases with the increase of harmonic order. To address the problem of inaccurate power metering under harmonic condition, this paper proposes a high-precision, wide-bandwidth, and low-cost multiplier topology. The accuracy of the multi-plier in the presence of harmonics is successfully verified through theoretical derivation and simulation. Furthermore, an experimental prototype of the proposed high-precision broadband low-cost multiplier has been built to verify the simulation results, which supports the effectiveness of the proposed high-precision broadband low-cost multiplier in this paper.
  Keywords: multiplier; harmonics; high-precision; wide-bandwidth; low-cost.
  DOI: 10.1504/IJDSDE.2025.10068722
   
  
• Technical Evaluation on Improved Hough Transform for Monitoring Traffic Sign Images under Depth Algorithm  
  by Jie Ding, Guotao Zhao 
  Abstract: The experiment drew the accuracy curve, training loss curve, and test loss curve of different traffic sign sizes and the network model after feature fusion, and compared the algorithm in this paper with the artificial neural network (ANN) algorithm and the random forest algorithm. The research results showed that the classification accuracy of the multi-scale model combining the three branch networks was as high as 99%; the classification accuracy of the extreme learning machine (ELM) classifier was better than that of the softmax and support vector machine (SVM) classifiers; compared with the ANN algorithm and the random forest algorithm, the classification time of the algorithm in this paper was reduced by 125 ms and 155 ms, respectively. The classification accuracy reached 99%, which lays the foundation for the innovation and development of traffic sign image processing technology.
  Keywords: Traffic Sign Image; Improved Hough Transform; Deep Algorithm; Multi-Scale Feature Fusion; Convolutional Neural Network.
  DOI: 10.1504/IJDSDE.2025.10068898
   
  
• Intelligent Optimisation of Self-Healing Strategy of Distribution Network based on Differential Evolution and Advanced Fractal  
  by Zhongqiang Zhou, Jianwei Ma, Yusong Huang, Ling Liang, Zhiqi Chen 
  Abstract: Traditional self-healing strategies for distribution networks are prone to getting stuck in local optima in complex power systems, resulting in the inability to find the globally optimal self-healing strategy. By introducing genetic algorithms and differential evolution optimisation, more effective self-healing strategies were sought to improve the robustness and anti-interference ability of the power system. The optimisation objective was to minimise the interruption time of power supply under the influence of faults, collect comprehensive data related to the power system, and apply genetic algorithm (GA), differential evolution (DE), and GA-DE to optimise the self-healing strategy of the distribution network. The experimental results indicate that the average convergence frequencies for GA, DE, and GA-DE were 716, 662, and 612, respectively. The average total power outage times were 195.3 seconds for GA, 178.8 seconds for DE, and 148.5 seconds for GA-DE. The GA-DE algorithm resulted in the fewest power outages over six years. By combining the strengths of GA and DE, the GA-DE algorithm enhances self-healing strategies in distribution networks, improving power system stability and reliability.
  Keywords: Distribution Network Self-healing; Strategy Optimization; Genetic Algorithm; Differential Evolution; Power Outage Time.
  DOI: 10.1504/IJDSDE.2025.10068926
   
  
• Nonlinear Programming Differential Equation Method for Architectural Landscape Spatial Structure Engineering in Dynamics Systems  
  by Kang Xiao, Yu Chen, Mei Xue 
  Abstract: In response to the problems of excessive model simplification and difficulty in parameter adjustment in current architectural landscape spatial structure planning, nonlinear programming differential equations (NPDEs) were applied to improve computational efficiency. Firstly, key features of architectural landscape spatial structure were defined, and nonlinear partial differential equations were used to simulate the evolution of spatial form over time. Secondly, architectural landscape observation data can be collected, and regression analysis can be used to identify key parameters of differential equations. Afterwards, the simulated annealing (SA) algorithm can be used to find the optimal parameter values. Then, the finite element method (FEM) can be applied to solve nonlinear differential equations. Finally, the paper presented the architectural landscape spatial structure under multiple feasible solutions (Pareto optimal solution set) and compared the key indicators of the paper's method with those of traditional models.
  Keywords: Architectural Landscape; Spatial Structure Engineering; Nonlinear Programming Differential Equations; Regression Analysis; Simulated Annealing.
  DOI: 10.1504/IJDSDE.2025.10069267
   
  
• Numerical Solution of Singular Autonomous Systems using the Fourth-Stage Geometric Mean Runge-Kutta Method  
  by Vijeyata Chauhan, Pankaj Kumar Srivastava 
  Abstract: The numerical treatment of singular problems is always seen to be intriguing, and its significance grows when it is raised in an autonomous system. This study proposes the development and implementation of a potent Runge-Kutta based fourth-stage explicit algorithm to numerically treat differential equations arising in the singular autonomous system. The basic properties of geometric mean have been brought into play to develop the algorithm. The convergence of the method has been established to prove the efficacy of the proposed technique. The consistency and stability of the method are also discussed. Two numerical illustrations are covered in the study and the results are compared with some other existing conventional methods, which confirms the importance of the method. The proposed method is found more efficient not only in terms of accuracy but also for applicability in first-order differential equations.
  Keywords: Explicit Runge-Kutta method; singular autonomous system; geometric mean; differential equations; increment function.
  DOI: 10.1504/IJDSDE.2025.10070393
   
  
• Group classification, exact solutions and conservation laws of (2 + 1)-dimensional time fractional Konopelchenko-Dubrovsky equation  
  by Jicheng Yu, Yuqiang Feng 
  Abstract: In this paper, Lie symmetry analysis method is applied to the (2 + 1)-dimensional time fractional Konopelchenko-Dubrovsky equations, which is an important model in physics. We obtained and classified all the Lie symmetries admitted by the equations according to the coefficients. Then we used the obtained group classification to reduce the (2 + 1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to some (1 + 1)-dimensional fractional partial differential equations with Erédlyi-Kober fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalisation of Noether operators are developed to construct the conservation laws for the equations studied.
  Keywords: Lie symmetry analysis; Riemann-Liouville fractional derivative; fractional modified Konopelchenko-Dubrovsky equations; Erdélyi-Kober fractional derivative; conservation laws.
  DOI: 10.1504/IJDSDE.2025.10067406
   
  
• Initial value solution of differential equations based on fuzzy system theory  
  by Xiaohui Zhang, Weiqiang Niu 
  Abstract: The research addresses the initial value problem of fuzzy differential equations, emphasising solution stability. By utilising fuzzy system theory and differential envelope theory, a relationship between differential envelope solutions and fuzzy differential equation solutions is established, and the stability of these solutions is analysed. The method is effectively applied to the stability analysis of uncertain dynamic systems, revealing that the relative error of the analytic solution y is under 0.2%, while the standard error of solution z is within 0.3%. The displacement of the midpoint of an elastic vertical plate and the radiation wave height for l/d = 4 show sensitivity to the stiffness coefficient and pulse amplitude, positively affecting vibration response and radiation height. Additionally, the decay rate for fixed boundary conditions is significantly faster than for the other conditions. The proposed method demonstrates high stability in solving the initial value problem of fuzzy differential equations.
  Keywords: fuzzy system theory; differential equation; initial value problem; stability; uncertain dynamical system.
  DOI: 10.1504/IJDSDE.2025.10068140
   
  
• Research on human-like solution method for graph isomorphic mathematical reasoning based on knowledge graph  
  by Yan Feng 
  Abstract: In the process of using knowledge graphs to assist deep learning in logical reasoning, there are problems with weak discriminative and generalisation abilities, as well as insufficient stability. A model for mathematical reasoning based on knowledge graph is proposed, which extracts classification features through graph isomorphism network and integrates the reverse to forward thinking approach to design a human like reasoning model for elementary mathematics. The innovation of the research lies in the use of a hierarchical structure in the design of the inference engine, which makes the logical layers relatively independent and highly modular, thereby improving computational efficiency. The results showed that the highest accuracy of the human like solution system constructed in the study was 94%, and the shortest time was 61.4 seconds. This indicates that the reasoning system can quickly and accurately solve elementary mathematics problems, providing a new method for education and teaching.
  Keywords: knowledge graph; triplet group extraction; elementary mathematics; human-like solution system; proximity algorithm.
  DOI: 10.1504/IJDSDE.2025.10068477
   
  
• Existence and stability analysis of neutral implicit fractional pantograph differential equations with non-local conditions using fixed-point theorems  
  by N. Annapoorani, D. Prabu 
  Abstract: This study explores the existence and stability of solutions for implicit neutral fractional pantograph differential equations with non-local conditions, utilising the recently introduced Ψ-Caputo fractional derivative. The research is driven by the increasing interest in fractional differential equations, particularly for their effectiveness in modelling complex systems characterised by memory and hereditary effects. This work addresses significant challenges associated with the combination of neutral terms, pantograph delays, and non-local boundary conditions an area that has received limited attention in the literature despite its relevance across various applied fields. To overcome these challenges, we apply fixed-point theorems, specifically the Banach and Schaefer fixed-point theorems, to establish new existence results for the solutions of the proposed equations. Additionally, we demonstrate the Ulam-Hyers stability of the problem, ensuring that minor perturbations in the initial data result in only small deviations in the solution, thus enhancing the robustness of the model. The theoretical findings are validated through an illustrative example, highlighting the practical relevance of the results and their potential applications in modelling real-world phenomena. This study not only advances the theoretical framework of fractional differential equations but also offers valuable insights for their application across a broad range of scientific and engineering disciplines.
  Keywords: non-local conditions; Ψ-Caputo fractional derivative; existence of solutions; fixed-point theorems; Ulam-Hyers stability; pantograph differential equations.
  DOI: 10.1504/IJDSDE.2024.10070260