Pub Date : 2024-07-04DOI: 10.3390/fractalfract8070400
Abdulaziz Alenazi, K. Mehrez
The main purpose of this paper is to study certain geometric properties of a class of analytic functions involving the Barnes–Mittag-Leffler function. The main mathematical tools are the monotonicity patterns of some class of functions associated with the gamma and digamma functions. Furthermore, some consequences and examples are presented.
{"title":"Certain Geometric Study Involving the Barnes–Mittag-Leffler Function","authors":"Abdulaziz Alenazi, K. Mehrez","doi":"10.3390/fractalfract8070400","DOIUrl":"https://doi.org/10.3390/fractalfract8070400","url":null,"abstract":"The main purpose of this paper is to study certain geometric properties of a class of analytic functions involving the Barnes–Mittag-Leffler function. The main mathematical tools are the monotonicity patterns of some class of functions associated with the gamma and digamma functions. Furthermore, some consequences and examples are presented.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141679404","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}
Pub Date : 2024-07-03DOI: 10.3390/fractalfract8070399
S. Galović, Aleksa I. Djordjevic, Bojan Z. Kovacevic, K. Djordjevic, Dalibor Chevizovich
In this paper, the time-resolved model of the photoacoustic signal for samples with a complex inner structure is derived including local non-equilibrium of structural elements with multiple degrees of freedom, i.e., structural entropy of the system. The local non-equilibrium is taken into account through the fractional operator. By analyzing the model for two types of time-dependent excitation, a very short pulse and a very long pulse, it is shown that the rates of non-equilibrium relaxations in complex samples can be measured by applying the derived model and time-domain measurements. Limitations of the model and further directions of its development are discussed.
{"title":"Influence of Local Thermodynamic Non-Equilibrium to Photothermally Induced Acoustic Response of Complex Systems","authors":"S. Galović, Aleksa I. Djordjevic, Bojan Z. Kovacevic, K. Djordjevic, Dalibor Chevizovich","doi":"10.3390/fractalfract8070399","DOIUrl":"https://doi.org/10.3390/fractalfract8070399","url":null,"abstract":"In this paper, the time-resolved model of the photoacoustic signal for samples with a complex inner structure is derived including local non-equilibrium of structural elements with multiple degrees of freedom, i.e., structural entropy of the system. The local non-equilibrium is taken into account through the fractional operator. By analyzing the model for two types of time-dependent excitation, a very short pulse and a very long pulse, it is shown that the rates of non-equilibrium relaxations in complex samples can be measured by applying the derived model and time-domain measurements. Limitations of the model and further directions of its development are discussed.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"138 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682541","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}
Pub Date : 2024-07-02DOI: 10.3390/fractalfract8070397
Asad Khan, Muhammad Awais Javeed, A. U. K. Niazi, Saadia Rehman, Yubin Zhong
This article investigates the resilient-based consensus analysis of fractional-order nonlinear leader-following systems with distributed and input lags. To enhance the practicality of the controller design, an incorporation of a disturbance term is proposed. Our modeling framework provides a more precise and flexible approach that considers the memory and heredity aspects of agent dynamics through the utilization of fractional calculus. Furthermore, the leader and follower equations of the system incorporate nonlinear functions to explore the resulting changes. The leader-following system is expressed by a weighted graph, which can be either undirected or directed. Analyzed using algebraic graph theory and the fractional-order Razumikhin technique, the case of leader-following consensus is presented algebraically. To increase robustness in multi-agent systems, input and distributive delays are used to accommodate communication delays and replicate real-time varying environments. This study lays the groundwork for developing control methods that are more robust and flexible in complex networked systems. It does so by advancing our understanding and practical application of fractional-order multi-agent systems. Additionally, experiments were conducted to show the effectiveness of the design in achieving consensus within the system.
{"title":"Robust Consensus Analysis in Fractional-Order Nonlinear Leader-Following Systems with Delays: Incorporating Practical Controller Design and Nonlinear Dynamics","authors":"Asad Khan, Muhammad Awais Javeed, A. U. K. Niazi, Saadia Rehman, Yubin Zhong","doi":"10.3390/fractalfract8070397","DOIUrl":"https://doi.org/10.3390/fractalfract8070397","url":null,"abstract":"This article investigates the resilient-based consensus analysis of fractional-order nonlinear leader-following systems with distributed and input lags. To enhance the practicality of the controller design, an incorporation of a disturbance term is proposed. Our modeling framework provides a more precise and flexible approach that considers the memory and heredity aspects of agent dynamics through the utilization of fractional calculus. Furthermore, the leader and follower equations of the system incorporate nonlinear functions to explore the resulting changes. The leader-following system is expressed by a weighted graph, which can be either undirected or directed. Analyzed using algebraic graph theory and the fractional-order Razumikhin technique, the case of leader-following consensus is presented algebraically. To increase robustness in multi-agent systems, input and distributive delays are used to accommodate communication delays and replicate real-time varying environments. This study lays the groundwork for developing control methods that are more robust and flexible in complex networked systems. It does so by advancing our understanding and practical application of fractional-order multi-agent systems. Additionally, experiments were conducted to show the effectiveness of the design in achieving consensus within the system.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"17 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141687898","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}
Pub Date : 2024-07-02DOI: 10.3390/fractalfract8070395
Muhammad Nadeem, Asad Khan, Muhammad Awais Javeed, Zhong Yubin
The Kawahara equation exhibits signal dispersion across lines of transmission and the production of unstable waves from the water in the broad wavelength area. This article explores the computational analysis for the approximate series of time fractional Kawahara (TFK) and modified Kawahara (TFMK) problems. We utilize the Shehu homotopy transform method (SHTM), which combines the Shehu transform (ST) with the homotopy perturbation method (HPM). He’s polynomials using HPM effectively handle the nonlinear terms. The derivatives of fractional order are examined in the Caputo sense. The suggested methodology remains unaffected by any assumptions, restrictions, or hypotheses on variables that could potentially pervert the fractional problem. We present numerical findings via visual representations to indicate the usability and performance of fractional order derivatives for depicting water waves in long-wavelength regions. The significance of our proposed scheme is demonstrated by the consistency of analytical results that align with the exact solutions. These derived results demonstrate that SHTM is an effective and powerful scheme for examining the results in the representation of series for time-fractional problems.
川原方程表现出信号在传输线上的分散，以及在宽波长区域从水中产生不稳定波。本文探讨了时间分数川原（TFK）和修正川原（TFMK）问题近似系列的计算分析。我们采用了谢胡同调变换法（SHTM），该方法结合了谢胡变换法（ST）和同调扰动法（HPM）。使用 HPM 的 He 多项式可以有效地处理非线性项。在卡普托意义上对分数阶导数进行了研究。所建议的方法不受变量的任何假设、限制或假定的影响，因为这些假设、限制或假定可能会使分数问题发生变化。我们通过可视化表示法展示了数值结果，以说明分数阶导数在描述长波长区域的水波时的可用性和性能。我们提出的方案的重要性体现在分析结果与精确解的一致性上。这些推导结果表明，SHTM 是一种有效而强大的方案，可用于检验时间分数问题的数列表示结果。
{"title":"Analytical Scheme for Time Fractional Kawahara and Modified Kawahara Problems in Shallow Water Waves","authors":"Muhammad Nadeem, Asad Khan, Muhammad Awais Javeed, Zhong Yubin","doi":"10.3390/fractalfract8070395","DOIUrl":"https://doi.org/10.3390/fractalfract8070395","url":null,"abstract":"The Kawahara equation exhibits signal dispersion across lines of transmission and the production of unstable waves from the water in the broad wavelength area. This article explores the computational analysis for the approximate series of time fractional Kawahara (TFK) and modified Kawahara (TFMK) problems. We utilize the Shehu homotopy transform method (SHTM), which combines the Shehu transform (ST) with the homotopy perturbation method (HPM). He’s polynomials using HPM effectively handle the nonlinear terms. The derivatives of fractional order are examined in the Caputo sense. The suggested methodology remains unaffected by any assumptions, restrictions, or hypotheses on variables that could potentially pervert the fractional problem. We present numerical findings via visual representations to indicate the usability and performance of fractional order derivatives for depicting water waves in long-wavelength regions. The significance of our proposed scheme is demonstrated by the consistency of analytical results that align with the exact solutions. These derived results demonstrate that SHTM is an effective and powerful scheme for examining the results in the representation of series for time-fractional problems.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"20 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141687559","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}
Pub Date : 2024-07-02DOI: 10.3390/fractalfract8070398
Yujun Cui, Chunyu Liang, Y. Zou
The paper studied high-order nonlinear fractional elastic equations that depend on low-order derivatives in nonlinearity and established the existence and uniqueness results by using the Leray–Schauder alternative theorem and Perov’s fixed point theorem on an appropriate space under mild assumptions. Examples are given to illustrate the key results.
{"title":"On Higher-Order Nonlinear Fractional Elastic Equations with Dependence on Lower Order Derivatives in Nonlinearity","authors":"Yujun Cui, Chunyu Liang, Y. Zou","doi":"10.3390/fractalfract8070398","DOIUrl":"https://doi.org/10.3390/fractalfract8070398","url":null,"abstract":"The paper studied high-order nonlinear fractional elastic equations that depend on low-order derivatives in nonlinearity and established the existence and uniqueness results by using the Leray–Schauder alternative theorem and Perov’s fixed point theorem on an appropriate space under mild assumptions. Examples are given to illustrate the key results.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"54 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688345","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}
Pub Date : 2024-07-02DOI: 10.3390/fractalfract8070396
Yadong Wang, Chong Liu
The fractional-order grey prediction model is widely recognized for its performance in time series prediction tasks with small sample characteristics. However, its parameter-estimation method, namely the least squares method, limits the predictive performance of the model and requires time to address the ill-conditioning of the system. To address these issues, this paper proposes a novel parameter-acquisition method treating structural parameters as hyperparameters, obtained through the marine predators optimization algorithm. The experimental analysis on three datasets validate the effectiveness of the method proposed in this paper.
{"title":"A New Fractional-Order Grey Prediction Model without a Parameter Estimation Process","authors":"Yadong Wang, Chong Liu","doi":"10.3390/fractalfract8070396","DOIUrl":"https://doi.org/10.3390/fractalfract8070396","url":null,"abstract":"The fractional-order grey prediction model is widely recognized for its performance in time series prediction tasks with small sample characteristics. However, its parameter-estimation method, namely the least squares method, limits the predictive performance of the model and requires time to address the ill-conditioning of the system. To address these issues, this paper proposes a novel parameter-acquisition method treating structural parameters as hyperparameters, obtained through the marine predators optimization algorithm. The experimental analysis on three datasets validate the effectiveness of the method proposed in this paper.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683957","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}
Pub Date : 2024-06-04DOI: 10.3390/fractalfract8060335
Yanxin Liu, Hong Zhang, Zhengchen Zhang, Luda Jing, Kouqi Liu
Distinguishing itself from marine shale formations, alkaline lake shale, as a significant hydrocarbon source rock and petroleum reservoir, exhibits distinct multifractal characteristics and evolutionary patterns. This study employs a combination of hydrous pyrolysis experimentation, nitrogen adsorption analysis, and multifractal theory to investigate the factors influencing pore heterogeneity and multifractal dimension during the maturation process of shale with abundant rich alkaline minerals. Utilizing partial least squares (PLS) analysis, a comparative examination is conducted, elucidating the disparate influence of mineralogical composition on their respective multifractal dimensions. The findings reveal a dynamic evolution of pore characteristics throughout the maturation process of alkaline lake shale, delineated into three distinct stages. Initially, in Stage 1 (200 °C to 300 °C), both ΔD and H demonstrate an incremental trend, rising from 1.2699 to 1.3 and from 0.8615 to 0.8636, respectively. Subsequently, in Stages 2 and 3, fluctuations are observed in the values of ΔD and D, while the H value undergoes a pronounced decline to 0.85. Additionally, the parameter D1 exhibits a diminishing trajectory across all stages, decreasing from 0.859 to 0.829, indicative of evolving pore structure characteristics throughout the maturation process. The distinct alkaline environment and mineral composition of alkaline lake shale engender disparate diagenetic effects during its maturation process compared with other shale varieties. Consequently, this disparity results in contrasting evolutionary trajectories in pore heterogeneity and multifractal characteristics. Specifically, multifractal characteristics of alkaline lake shale are primarily influenced by quartz, potassium feldspar, clay minerals, and alkaline minerals.
碱湖页岩有别于海相页岩层，作为重要的烃源岩和石油储层，表现出明显的多分形特征和演化规律。本研究结合含水热解实验、氮吸附分析和多分形理论，研究了富含碱性矿物的页岩成熟过程中孔隙异质性和多分形维度的影响因素。利用偏最小二乘法（PLS）分析进行比较研究，阐明了矿物成分对各自多分形维度的不同影响。研究结果表明，在碱性湖页岩的整个成熟过程中，孔隙特征发生了动态演变，并划分为三个不同的阶段。起初，在第一阶段（200 °C至300 °C），ΔD和H均呈现递增趋势，分别从1.2699升至1.3和从0.8615升至0.8636。随后，在第二和第三阶段，ΔD 和 D 值出现波动，而 H 值则明显下降至 0.85。此外，参数 D1 在所有阶段都呈递减轨迹，从 0.859 降至 0.829，表明孔隙结构特征在整个成熟过程中不断演变。与其他页岩品种相比，碱性湖页岩独特的碱性环境和矿物成分在其成熟过程中产生了不同的成岩作用。因此，这种差异导致孔隙异质性和多分形特征呈现出截然不同的演化轨迹。具体来说，碱性湖页岩的多分形特征主要受石英、钾长石、粘土矿物和碱性矿物的影响。
{"title":"Quantifying the Pore Heterogeneity of Alkaline Lake Shale during Hydrous Pyrolysis by Using the Multifractal Method","authors":"Yanxin Liu, Hong Zhang, Zhengchen Zhang, Luda Jing, Kouqi Liu","doi":"10.3390/fractalfract8060335","DOIUrl":"https://doi.org/10.3390/fractalfract8060335","url":null,"abstract":"Distinguishing itself from marine shale formations, alkaline lake shale, as a significant hydrocarbon source rock and petroleum reservoir, exhibits distinct multifractal characteristics and evolutionary patterns. This study employs a combination of hydrous pyrolysis experimentation, nitrogen adsorption analysis, and multifractal theory to investigate the factors influencing pore heterogeneity and multifractal dimension during the maturation process of shale with abundant rich alkaline minerals. Utilizing partial least squares (PLS) analysis, a comparative examination is conducted, elucidating the disparate influence of mineralogical composition on their respective multifractal dimensions. The findings reveal a dynamic evolution of pore characteristics throughout the maturation process of alkaline lake shale, delineated into three distinct stages. Initially, in Stage 1 (200 °C to 300 °C), both ΔD and H demonstrate an incremental trend, rising from 1.2699 to 1.3 and from 0.8615 to 0.8636, respectively. Subsequently, in Stages 2 and 3, fluctuations are observed in the values of ΔD and D, while the H value undergoes a pronounced decline to 0.85. Additionally, the parameter D1 exhibits a diminishing trajectory across all stages, decreasing from 0.859 to 0.829, indicative of evolving pore structure characteristics throughout the maturation process. The distinct alkaline environment and mineral composition of alkaline lake shale engender disparate diagenetic effects during its maturation process compared with other shale varieties. Consequently, this disparity results in contrasting evolutionary trajectories in pore heterogeneity and multifractal characteristics. Specifically, multifractal characteristics of alkaline lake shale are primarily influenced by quartz, potassium feldspar, clay minerals, and alkaline minerals.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"10 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141266666","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}
Pub Date : 2024-06-04DOI: 10.3390/fractalfract8060336
Aleksander A. Stanislavsky, Aleksander Weron
The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows for the detection of jumps in segmented trajectories with non-Gaussian confined parts. The value of each parameter indicates the contribution of confined segments. Non-Gaussian features in mRNA trajectories are attributed to trajectory segmentation. Each segment can be in one of the following diffusion modes: free diffusion, confined motion, and immobility. When free diffusion segments alternate with confined or immobile segments, the mean square displacement of the segmented trajectory resembles subdiffusion. Confined segments have both Gaussian (normal) and non-Gaussian statistics. If random trajectories are estimated as FLSM, they can exhibit either subdiffusion or Lévy diffusion. This approach can be useful for analyzing empirical data with non-Gaussian behavior, and statistical classification of diffusion trajectories helps reveal anomalous dynamics.
{"title":"Fractional Lévy Stable Motion from a Segmentation Perspective","authors":"Aleksander A. Stanislavsky, Aleksander Weron","doi":"10.3390/fractalfract8060336","DOIUrl":"https://doi.org/10.3390/fractalfract8060336","url":null,"abstract":"The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows for the detection of jumps in segmented trajectories with non-Gaussian confined parts. The value of each parameter indicates the contribution of confined segments. Non-Gaussian features in mRNA trajectories are attributed to trajectory segmentation. Each segment can be in one of the following diffusion modes: free diffusion, confined motion, and immobility. When free diffusion segments alternate with confined or immobile segments, the mean square displacement of the segmented trajectory resembles subdiffusion. Confined segments have both Gaussian (normal) and non-Gaussian statistics. If random trajectories are estimated as FLSM, they can exhibit either subdiffusion or Lévy diffusion. This approach can be useful for analyzing empirical data with non-Gaussian behavior, and statistical classification of diffusion trajectories helps reveal anomalous dynamics.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"4 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267406","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}
Pub Date : 2024-06-03DOI: 10.3390/fractalfract8060333
Hui Zhang, Ahmadjan Muhammadhaji
In this study, a class of delayed fractional-order predation models with disease and cannibalism in the prey was studied. In addition, we considered the prey stage structure and the refuge effect. A Holling type-II functional response function was used to describe predator–prey interactions. First, the existence and uniform boundedness of the solutions of the systems without delay were proven. The local stability of the equilibrium point was also analyzed. Second, we used the digestion delay of predators as a bifurcation parameter to determine the conditions under which Hopf bifurcation occurs. Finally, a numerical simulation was performed to validate the obtained results. Numerical simulations have shown that cannibalism contributes to the elimination of disease in diseased prey populations. In addition, the size of the bifurcation point τ0 decreased with an increase in the fractional order, and this had a significant effect on the stability of the system.
在这项研究中，我们研究了一类延迟分数阶捕食模型，该模型中的猎物存在疾病和食人现象。此外，我们还考虑了猎物的阶段结构和避难所效应。采用霍林 II 型功能响应函数来描述捕食者与猎物之间的相互作用。首先，证明了无延迟系统解的存在性和均匀有界性。同时还分析了平衡点的局部稳定性。其次，我们利用捕食者的消化延迟作为分岔参数，确定了发生霍普夫分岔的条件。最后，我们进行了数值模拟来验证所获得的结果。数值模拟表明，食人行为有助于消除患病猎物种群中的疾病。此外，分岔点 τ0 的大小随着分数阶数的增加而减小，这对系统的稳定性有显著影响。
{"title":"Dynamics of a Delayed Fractional-Order Predator–Prey Model with Cannibalism and Disease in Prey","authors":"Hui Zhang, Ahmadjan Muhammadhaji","doi":"10.3390/fractalfract8060333","DOIUrl":"https://doi.org/10.3390/fractalfract8060333","url":null,"abstract":"In this study, a class of delayed fractional-order predation models with disease and cannibalism in the prey was studied. In addition, we considered the prey stage structure and the refuge effect. A Holling type-II functional response function was used to describe predator–prey interactions. First, the existence and uniform boundedness of the solutions of the systems without delay were proven. The local stability of the equilibrium point was also analyzed. Second, we used the digestion delay of predators as a bifurcation parameter to determine the conditions under which Hopf bifurcation occurs. Finally, a numerical simulation was performed to validate the obtained results. Numerical simulations have shown that cannibalism contributes to the elimination of disease in diseased prey populations. In addition, the size of the bifurcation point τ0 decreased with an increase in the fractional order, and this had a significant effect on the stability of the system.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"31 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141270488","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}
Pub Date : 2024-06-03DOI: 10.3390/fractalfract8060334
Abdul Wadood, Al-Fahad Yousaf, Aadel M. Alatwi
This paper addresses the enhancement of multiple Unmanned Aerial Vehicle (UAV) swarm formation control in challenging terrains through the novel fractional memetic computing approach known as fractional-order velocity-pausing particle swarm optimization (FO-VPPSO). Existing particle swarm optimization (PSO) algorithms often suffer from premature convergence and an imbalanced exploration–exploitation trade-off, which limits their effectiveness in complex optimization problems such as UAV swarm control in rugged terrains. To overcome these limitations, FO-VPPSO introduces an adaptive fractional order β and a velocity pausing mechanism, which collectively enhance the algorithm’s adaptability and robustness. This study leverages the advantages of a meta-heuristic computing approach; specifically, fractional-order velocity-pausing particle swarm optimization is utilized to optimize the flying path length, mitigate the mountain terrain costs, and prevent collisions within the UAV swarm. Leveraging fractional-order dynamics, the proposed hybrid algorithm exhibits accelerated convergence rates and improved solution optimality compared to traditional PSO methods. The methodology involves integrating terrain considerations and diverse UAV control parameters. Simulations under varying conditions, including complex terrains and dynamic threats, substantiate the effectiveness of the approach, resulting in superior fitness functions for multi-UAV swarms. To validate the performance and efficiency of the proposed optimizer, it was also applied to 13 benchmark functions, including uni- and multimodal functions in terms of the mean average fitness value over 100 independent trials, and furthermore, an improvement at percentages of 29.05% and 2.26% is also obtained against PSO and VPPSO in the case of the minimum flight length, as well as 16.46% and 1.60% in mountain terrain costs and 55.88% and 31.63% in collision avoidance. This study contributes valuable insights to the optimization challenges in UAV swarm-formation control, particularly in demanding terrains. The FO-VPPSO algorithm showcases potential advancements in swarm intelligence for real-world applications.
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