Fractal and Fractional最新文献_第10页

Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations 一些非常规分式 Sturm-Liouville 方程的存在性和唯一性

Fractal and Fractional Pub Date : 2024-03-03 DOI: 10.3390/fractalfract8030148

Leila Gholizadeh Zivlaei, A. Mingarelli

引用次数: 0

Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition 自适应系数有限差分频域法求解带吸收边界条件的时分数卡塔尼奥方程

Fractal and Fractional Pub Date : 2024-02-29 DOI: 10.3390/fractalfract8030146

Wenhao Xu, Jing Ba, Jianxiong Cao, Cong Luo

{"title":"Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition","authors":"Wenhao Xu, Jing Ba, Jianxiong Cao, Cong Luo","doi":"10.3390/fractalfract8030146","DOIUrl":"https://doi.org/10.3390/fractalfract8030146","url":null,"abstract":"The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"5 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140410304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Applications of Fractional Order Logistic Grey Models for Carbon Emission Forecasting 分数阶逻辑灰色模型在碳排放预测中的应用

Fractal and Fractional Pub Date : 2024-02-29 DOI: 10.3390/fractalfract8030145

Xiaoqiang He, Yuxin Song, Fengmin Yu, Huiming Duan

{"title":"Applications of Fractional Order Logistic Grey Models for Carbon Emission Forecasting","authors":"Xiaoqiang He, Yuxin Song, Fengmin Yu, Huiming Duan","doi":"10.3390/fractalfract8030145","DOIUrl":"https://doi.org/10.3390/fractalfract8030145","url":null,"abstract":"In recent years, global attention to carbon emissions has increased, becoming one of the main drivers of global climate change. Accurate prediction of carbon emission trends in small and medium-sized countries and scientific regulation of carbon emissions can provide theoretical support and policy references for the effective and rational use of energy and the promotion of the coordinated development of energy, environment, and economy. This paper establishes a grey prediction model using the classical Logistic mathematical model in a determined environment to investigate the carbon emission system. At the same time, we use the basic principle of fractional-order accumulation to establish a grey prediction model with fractional-order Logistic and obtain the parameter estimation and time-response equation of the new model by solving the model through the theory related to fractional-order operators. The particle swarm optimization algorithm is used to complete the optimization process of the order of the fractional order grey prediction model and obtain the optimal model order. Then, the new model is applied to predict carbon emissions in five medium-emission countries: Ethiopia, Djibouti, Ghana, Belgium, and Austria. The new model shows better advantages in the validity analysis process, and the simulation results indicate that the new model proposed in this paper has stronger stability and better simulation and prediction accuracy than other comparative models, proving the model’s validity. Finally, the model is used to forecast the carbon emissions of these five countries for the five years of 2021–2025, and the results are analyzed, and relevant policy recommendations are made.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"22 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140414163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Existence of Solutions for w-Weighted ψ-Hilfer Fractional Differential Inclusions of Order μ ∈ (1, 2) with Non-Instantaneous Impulses in Banach Spaces 巴拿赫空间中具有非瞬时脉冲的秩 μ∈ (1, 2) 的 w 加权ψ-希尔费分式微分结论的解的存在性

Fractal and Fractional Pub Date : 2024-02-29 DOI: 10.3390/fractalfract8030144

Zainab Alsheekhhussain, Ahmad Gamal Ibrahim, M. M. Al-sawalha, Yousef Jawarneh

引用次数: 0

Characterization of the Fine-Scale Evolution of Damage in Shale under the Influence of Two-Way Stress Differences Based on CT Images and Fractal Theory—The Example of the Anba Dyke in the Wufeng–Longmaxi Formation 基于 CT 图像和分形理论的双向应力差影响下页岩损伤的精细演化特征--以五峰-龙马溪地层中的安坝堤坝为例

Fractal and Fractional Pub Date : 2024-02-29 DOI: 10.3390/fractalfract8030142

Baofeng Lan, Ruidong Yang, Zhonghu Wu, Haishen Jiang, Xinzheng Li

{"title":"Characterization of the Fine-Scale Evolution of Damage in Shale under the Influence of Two-Way Stress Differences Based on CT Images and Fractal Theory—The Example of the Anba Dyke in the Wufeng–Longmaxi Formation","authors":"Baofeng Lan, Ruidong Yang, Zhonghu Wu, Haishen Jiang, Xinzheng Li","doi":"10.3390/fractalfract8030142","DOIUrl":"https://doi.org/10.3390/fractalfract8030142","url":null,"abstract":"To better understand the influence of different levels of two-way stress differences on the development of damage in Anchang diametral laminar shale in the northern Qianbei area, a numerical model of laminar shale with a representative fine-scale structure was established by using RFPA3D-CT. A triaxial compression test was conducted; a three-dimensional mesoscale fracture box dimension algorithm based on digital images was generated by using MATLAB R2020b; and the fractal characteristics were quantitatively analyzed. The results showed that under the influence of the horizontal stress ratio and two-way stress, the greater the two-way stress is, the more notable the plastic characteristics of specimen damage are, and the higher the residual strength is. The specimens with lower two-way stress exhibited obvious brittle damage characteristics. The difficulty degree of complex fracture network formation increased with the increase in the horizontal tension ratio, and the degree of increase in the fracture network complexity gradually decreased. At a horizontal stress ratio of 1.25, the fractal dimension was the highest, which indicates that the cracks were the most pronounced. Fracture formation after specimen damage was the most common phenomenon. Under the condition of a lower horizontal stress ratio, a large number of fracture structures could be generated in shale specimens after damage, promoting the expansion of natural fractures.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"30 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140413183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Transient Dynamics of a Fractional Fisher Equation 分式费雪方程的瞬态动力学

Fractal and Fractional Pub Date : 2024-02-29 DOI: 10.3390/fractalfract8030143

E. C. Gabrick, P. Protachevicz, Diogo L. M. Souza, José Trobia, E. Sayari, F. Borges, M. Lenzi, I. L. Caldas, Antonio M. Batista, E. Lenzi

{"title":"Transient Dynamics of a Fractional Fisher Equation","authors":"E. C. Gabrick, P. Protachevicz, Diogo L. M. Souza, José Trobia, E. Sayari, F. Borges, M. Lenzi, I. L. Caldas, Antonio M. Batista, E. Lenzi","doi":"10.3390/fractalfract8030143","DOIUrl":"https://doi.org/10.3390/fractalfract8030143","url":null,"abstract":"We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by u(0,t)−2, our results show that the solution reaches a steady state governed by the parameters present in the logistic function in Fisher’s equation. The initial transient is an anomalous diffusion process, but a power law cannot describe the whole transient. In this sense, the main novelty of this work is to show that a q-exponential function gives a better description of the transient dynamics. In addition to this result, we extend the Fisher equation via non-integer operators. As a fractional definition, we employ the Caputo fractional derivative and use a discretized system for the numerical approach according to finite difference schemes. We consider the numerical solutions in three scenarios: fractional differential operators acting in time, space, and in both variables. Our results show that the time to reach the steady solution strongly depends on the fractional order of the differential operator, with more influence by the time operator. Our main finding shows that a generalized q-exponential, present in the Tsallis formalism, describes the transient dynamics. The adjustment parameters of the q-exponential depend on the fractional order, connecting the generalized thermostatistics with the anomalous relaxation promoted by the fractional operators in time and space.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"1983 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140416772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Changes in Pore Structure and Fractal Characteristics of Solvents Pretreated High-Rank Coal under Supercritical CO2 超临界二氧化碳条件下溶剂预处理高阶煤的孔隙结构和分形特征变化

Fractal and Fractional Pub Date : 2024-02-28 DOI: 10.3390/fractalfract8030141

Yong Li, Xiaodong Zhang, Yijuan Sun, Zhen Wang, Shuo Zhang, Binghui Li

{"title":"Changes in Pore Structure and Fractal Characteristics of Solvents Pretreated High-Rank Coal under Supercritical CO2","authors":"Yong Li, Xiaodong Zhang, Yijuan Sun, Zhen Wang, Shuo Zhang, Binghui Li","doi":"10.3390/fractalfract8030141","DOIUrl":"https://doi.org/10.3390/fractalfract8030141","url":null,"abstract":"CO2 injection in coal seams, which is a significant initiative to mitigate environmental problems caused by greenhouse gases, often leads a sequence of changes in the physical properties of coal reservoirs. To look into how the pore structure changes in the process of CO2 sequestration, we selected fresh coal from Huoerxinhe coal mine in China as the object. Then, acid treatment and SC-CO2 extraction were used to dissolve Organic and inorganic components in coal. Thus, by using SEM, LTGA-N2 apparatus and XRD, the characteristics of pore parameter and fractal dimension variation were discussed. The research results show that, the APS of samples THF, HCL-HF and Y-C increase, while the total PV decreases and the pore connectivity deteriorates. The pore connectivity of Samples THF and HCL-HF is improved (THF-C, HCL-HF-C), but the total pore volume continuously reduces. In addition, solvents treatment and SC-CO2 extraction mainly act on the microporous fraction. After solvents pretreatment, the changes in the pore size distribution curves are mainly manifested in the reduction of number of micropores, especially in the micropores around 3–4 nm. There is a small increase in micropores for samples Y-C and HCL-HF-C, with the pore size mainly concentrated around 4 nm, while the pores of the sample THF-C mainly show an increase within the scope of 3–16 nm. Generally, solvent pretreatment and SC-CO2 extraction help to simplify pore structure. However, the sample HCL-HF-C shows opposite change characteristics. In a short period of time, the larger pore fractal dimension, the less beneficial it is to the flow of CO2, while pore fractal dimension becomes progressively less useful in assessing pore connectivity with increasing time.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"105 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140422749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enhancing Microgrid Inverter-Integrated Charging Station Performance through Optimization of Fractional-Order PI Controller Using the One-to-One Sine Cosine Algorithm 利用一对一正弦余弦算法优化分数阶 PI 控制器，提高微电网逆变器集成充电站的性能

Fractal and Fractional Pub Date : 2024-02-28 DOI: 10.3390/fractalfract8030139

Abdallah Aldosary

{"title":"Enhancing Microgrid Inverter-Integrated Charging Station Performance through Optimization of Fractional-Order PI Controller Using the One-to-One Sine Cosine Algorithm","authors":"Abdallah Aldosary","doi":"10.3390/fractalfract8030139","DOIUrl":"https://doi.org/10.3390/fractalfract8030139","url":null,"abstract":"This paper is dedicated to optimizing the functionality of Microgrid-Integrated Charging Stations (MICCS) through the implementation of a new control strategy, specifically the fractional-order proportional-integral (FPI) controller, aided by a hybrid optimization algorithm. The primary goal is to elevate the efficiency and stability of the MICCS-integrated inverter, ensuring its seamless integration into modern energy ecosystems. The MICCS system considered here comprises a PV array as the primary electrical power source, complemented by a proton exchange membrane fuel cell as a supporting power resource. Additionally, it includes a battery system and an electric vehicle charging station. The optimization model is formulated with the objective of minimizing the integral of square errors in both the DC-link voltage and grid current while also reducing total harmonic distortion. To enhance the precision of control parameter estimation, a hybrid of the one-to-one optimizer and sine cosine algorithm (HOOBSCA) is introduced. This hybrid approach improves the exploitation and exploration characteristics of individual algorithms. Different meta-heuristic algorithms are tested against HOOBSCA in different case studies to see how well it tunes FPI settings. Findings demonstrate that the suggested method improves the integrated inverters’ transient and steady-state performance, confirming its improved performance in generating high-quality solutions. The best fitness value achieved by the proposed optimizer was 3.9109, outperforming the other algorithms investigated in this paper. The HOOBSCA-based FPI successfully improved the response of the DC-link voltage, with a maximum overshooting not exceeding 8.5% compared to the other algorithms employed in this study.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"15 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140418525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Power Quality Conditioners-Based Fractional-Order PID Controllers Using Hybrid Jellyfish Search and Particle Swarm Algorithm for Power Quality Enhancement 基于电能质量调节器的分数阶 PID 控制器，采用混合水母搜索和粒子群算法提高电能质量

Fractal and Fractional Pub Date : 2024-02-28 DOI: 10.3390/fractalfract8030140

Abdallah Aldosary

{"title":"Power Quality Conditioners-Based Fractional-Order PID Controllers Using Hybrid Jellyfish Search and Particle Swarm Algorithm for Power Quality Enhancement","authors":"Abdallah Aldosary","doi":"10.3390/fractalfract8030140","DOIUrl":"https://doi.org/10.3390/fractalfract8030140","url":null,"abstract":"Power quality (PQ) is a major issue in today’s electrical system that affects both utilities and customers. The proliferation of power electronics devices, smart grid technology, and renewable energy sources (RES) have all contributed to the emergence of PQ concerns in today’s power system. The Unified Power Quality Conditioner (UPQC) is a versatile tool that can be used to fix distribution grid issues caused by irregular voltage, current, or frequency. Several tuning parameters, however, restrict the effectiveness of the Fractional-Order Proportional Integral Derivative (FOPID) control technique, which is proposed to improve UPQC performance. To move beyond these restrictions and find the optimal solution for the FOPID controller problem, a hybrid optimization strategy called the Hybrid Jellyfish Search Optimizer and Particle Swarm Optimizer (HJSPSO) is employed. To meet the load requirement during PQ issue periods, the suggested model incorporates a renewable energy source into the grid system. Whether the load is linear or non-linear, the design maintains PQ problems to a minimum. Furthermore, the FOPID control technique is compared with other controllers. Results show that grid-connected RES systems using the proposed FOPID control approach for UPQC have fewer PQ problems. The presented UPQC with HJSPSO strategy significantly outperformed, with the shortest computing time of 127.474 s and an objective function value of 1.423.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"325 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140417235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Impact of Sentinel-1-Corrected Fractal Roughness on Soil Moisture Retrievals 哨兵 1 号校正分形粗糙度对土壤水分检索的影响

Fractal and Fractional Pub Date : 2024-02-27 DOI: 10.3390/fractalfract8030137

Ju Hyoung Lee, Hyun-Cheol Kim

{"title":"The Impact of Sentinel-1-Corrected Fractal Roughness on Soil Moisture Retrievals","authors":"Ju Hyoung Lee, Hyun-Cheol Kim","doi":"10.3390/fractalfract8030137","DOIUrl":"https://doi.org/10.3390/fractalfract8030137","url":null,"abstract":"Fractals are widely recognized as one of the best geometric models to depict soil roughness on various scales from tillage to micro-topography smaller than radar wavelength. However, most fractal approaches require an additional geometric description of experimental sites to be analysed by existing radiative transfer models. For example, fractal dimension or spectral parameter is often related to root-mean-square (RMS) height to be characterized as the microwave surface. However, field measurements hardly represent multi-scale roughness. In this study, we rescaled Power Spectral Density with Synthetic Aperture Radar (SAR)-inverted rms height, and estimated non-stationary fractal roughness to accommodate multi-scale roughness into a radiative transfer model structure. As a result, soil moisture was retrieved over the Yanco site in Australia. Local validation shows that the Integral Equation Model (IEM) poorly simulated backscatters using inverted roughness as compared to fractal roughness even in anisotropic conditions. This is considered due to a violation of time-invariance assumption used for inversion. Spatial analysis also shows that multi-scale fractal roughness better illustrated the hydrologically reasonable backscattering partitioning, as compared to inverted roughness. Fractal roughness showed a greater contribution of roughness to backscattering in dry conditions. Differences between IEM backscattering and measurement were lower, even when the isotropic assumption of the fractal model was violated. In wet conditions, the contribution of soil moisture to backscattering was shown more clearly by fractal roughness. These results suggest that the multi-scale fractal roughness can be better adapted to the IEM even in anisotropic conditions than the inversion to assume time-invariance of roughness.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"51 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140425470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0