Pub Date : 2024-06-05DOI: 10.3390/fractalfract8060338
Gustavo E. Ceballos Benavides, M. Duarte-Mermoud, Marcos E. Orchard, Alfonso Ehijo
This study presents a comparative analysis of classical model reference adaptive control (IO-DMRAC) and its fractional-order counterpart (FO-DMRAC), which are applied to the pitch-rate control of an F-16 aircraft longitudinal model. The research demonstrates a significant enhancement in control performance with fractional-order adaptive control. Notably, the FO-DMRAC achieves lower performance indices such as the Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) and eliminates system output oscillations during transient periods. This study marks the pioneering application of FO-DMRAC in aircraft pitch-rate control within the literature. Through simulations on an F-16 short-period model with a relative degree of 1, the FO-DMRAC design is assessed under specific flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the study ensures the boundedness of all signals, including internal ones such as ω(t).
{"title":"Enhancing the Pitch-Rate Control Performance of an F-16 Aircraft Using Fractional-Order Direct-MRAC Adaptive Control","authors":"Gustavo E. Ceballos Benavides, M. Duarte-Mermoud, Marcos E. Orchard, Alfonso Ehijo","doi":"10.3390/fractalfract8060338","DOIUrl":"https://doi.org/10.3390/fractalfract8060338","url":null,"abstract":"This study presents a comparative analysis of classical model reference adaptive control (IO-DMRAC) and its fractional-order counterpart (FO-DMRAC), which are applied to the pitch-rate control of an F-16 aircraft longitudinal model. The research demonstrates a significant enhancement in control performance with fractional-order adaptive control. Notably, the FO-DMRAC achieves lower performance indices such as the Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) and eliminates system output oscillations during transient periods. This study marks the pioneering application of FO-DMRAC in aircraft pitch-rate control within the literature. Through simulations on an F-16 short-period model with a relative degree of 1, the FO-DMRAC design is assessed under specific flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the study ensures the boundedness of all signals, including internal ones such as ω(t).","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141386119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.3390/fractalfract8050293
Q. Ain, Anwarud Din, Xiaoli Qiang, Zheng Kou
In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.
{"title":"Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise","authors":"Q. Ain, Anwarud Din, Xiaoli Qiang, Zheng Kou","doi":"10.3390/fractalfract8050293","DOIUrl":"https://doi.org/10.3390/fractalfract8050293","url":null,"abstract":"In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140967726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.3390/fractalfract8050294
Shaolong Zeng, Yangfan Hu, Shijing Tan, Biao Wang
We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.
{"title":"Critical Exponents and Universality for Fractal Time Processes above the Upper Critical Dimensionality","authors":"Shaolong Zeng, Yangfan Hu, Shijing Tan, Biao Wang","doi":"10.3390/fractalfract8050294","DOIUrl":"https://doi.org/10.3390/fractalfract8050294","url":null,"abstract":"We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140970961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.3390/fractalfract8050292
R. Alsaedi
In this paper, we will study a singular problem involving the fractional (q1(x,.)-q2(x,.))-Laplacian operator in the whole space RN,(N≥2). More precisely, we combine the variational method with monotonicity arguments to prove that the associated functional energy admits a critical point, which is a weak solution for such a problem.
{"title":"Existence Results Related to a Singular Fractional Double-Phase Problem in the Whole Space","authors":"R. Alsaedi","doi":"10.3390/fractalfract8050292","DOIUrl":"https://doi.org/10.3390/fractalfract8050292","url":null,"abstract":"In this paper, we will study a singular problem involving the fractional (q1(x,.)-q2(x,.))-Laplacian operator in the whole space RN,(N≥2). More precisely, we combine the variational method with monotonicity arguments to prove that the associated functional energy admits a critical point, which is a weak solution for such a problem.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.3390/fractalfract8050295
H. Serag, Areej A. Almoneef, Mahmoud El-Badawy, Abd-Allah Hyder
This paper studies distributed optimal control for non-cooperative systems involving time-fractional hyperbolic operators. Through the application of the Lax–Milgram theorem, we confirm the existence and uniqueness of weak solutions. Central to our approach is the utilization of the linear quadratic cost functional, which is meticulously crafted to encapsulate the interplay between the system’s state and control variables. This functional serves as a pivotal tool in imposing constraints on the dynamic system under consideration, facilitating a nuanced understanding of its controllability. Using the Euler–Lagrange first-order optimality conditions with an adjoint problem defined by means of the right-time fractional derivative in the Caputo sense, we obtain an optimality system for the optimal control. Finally, some examples are analyzed.
{"title":"Distributed Control for Non-Cooperative Systems Governed by Time-Fractional Hyperbolic Operators","authors":"H. Serag, Areej A. Almoneef, Mahmoud El-Badawy, Abd-Allah Hyder","doi":"10.3390/fractalfract8050295","DOIUrl":"https://doi.org/10.3390/fractalfract8050295","url":null,"abstract":"This paper studies distributed optimal control for non-cooperative systems involving time-fractional hyperbolic operators. Through the application of the Lax–Milgram theorem, we confirm the existence and uniqueness of weak solutions. Central to our approach is the utilization of the linear quadratic cost functional, which is meticulously crafted to encapsulate the interplay between the system’s state and control variables. This functional serves as a pivotal tool in imposing constraints on the dynamic system under consideration, facilitating a nuanced understanding of its controllability. Using the Euler–Lagrange first-order optimality conditions with an adjoint problem defined by means of the right-time fractional derivative in the Caputo sense, we obtain an optimality system for the optimal control. Finally, some examples are analyzed.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140969906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.3390/fractalfract8050290
Jiaojiao Ren, Can Zhao, Jianying Xiao, Renfu Luo, Nanrong He
This paper investigates the problem of exponential H∞ output control for switching fuzzy systems, considering both impulse and non-impulse scenarios. Unlike previous research, where the average dwell time (ADT: τa) and the upper bound of inter-event intervals (IEIs: T) satisfy the condition τa≥lnμ+(α+β)Tα=lnμ+βTα+T, implying that frequent switching is difficult to achieve, this paper demonstrates that by adopting the mode-dependent event-triggered mechanism (ETM) and a switching law, frequent switching is indeed achieved. Moreover, the question of deriving the normal L2 norm constraint is solved through the ADT method, although only a weighted L2 norm constraint was obtained previously. Additionally, by constructing a controller-mode-dependent Lyapunov function and adopting logarithmic quantizers, the sufficient criteria of exponential H∞ output control problem are presented. The validity of established results is demonstrated by a given numerical simulation.
{"title":"Exponential H∞ Output Control for Switching Fuzzy Systems via Event-Triggered Mechanism and Logarithmic Quantization","authors":"Jiaojiao Ren, Can Zhao, Jianying Xiao, Renfu Luo, Nanrong He","doi":"10.3390/fractalfract8050290","DOIUrl":"https://doi.org/10.3390/fractalfract8050290","url":null,"abstract":"This paper investigates the problem of exponential H∞ output control for switching fuzzy systems, considering both impulse and non-impulse scenarios. Unlike previous research, where the average dwell time (ADT: τa) and the upper bound of inter-event intervals (IEIs: T) satisfy the condition τa≥lnμ+(α+β)Tα=lnμ+βTα+T, implying that frequent switching is difficult to achieve, this paper demonstrates that by adopting the mode-dependent event-triggered mechanism (ETM) and a switching law, frequent switching is indeed achieved. Moreover, the question of deriving the normal L2 norm constraint is solved through the ADT method, although only a weighted L2 norm constraint was obtained previously. Additionally, by constructing a controller-mode-dependent Lyapunov function and adopting logarithmic quantizers, the sufficient criteria of exponential H∞ output control problem are presented. The validity of established results is demonstrated by a given numerical simulation.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140975378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.3390/fractalfract8050291
Muhammad Riaz, Zareen A. Khan, Sadique Ahmad, A. Ateya
Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method.
{"title":"Fractional-Order Dynamics in Epidemic Disease Modeling with Advanced Perspectives of Fractional Calculus","authors":"Muhammad Riaz, Zareen A. Khan, Sadique Ahmad, A. Ateya","doi":"10.3390/fractalfract8050291","DOIUrl":"https://doi.org/10.3390/fractalfract8050291","url":null,"abstract":"Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-13DOI: 10.3390/fractalfract8050289
Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, M. M. Al-Sawalha, Khudhayr A. Rashedi
The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.
本研究的目的是，当线性项是强连续余弦族的无穷小生成器，而非线性项是多值函数时，在无穷维度的巴纳赫空间中，对涉及阶数为μ∈(1,2)的具有非瞬时脉冲的w加权、Φ-Hilfer、分数导数的半线性微分包含的温和解，获得新颖而有趣的结果。首先，我们确定了所考虑的半线性微分包含的温和解函数公式。然后，我们给出了确保温和解集不空或紧凑的充分条件。通过使用 w 加权 Φ 拉普拉斯变换、w 加权 ψ 卷积和非紧凑性度量的特性，我们可以得到所需的结果。由于 w 加权 Φ-Hilfer 算子包括众所周知的分数微分算子类型，我们的结果概括了文献中的几个最新结果。此外，我们的结果是新颖的，因为以前没有人研究过这些类型的半线性微分夹杂。最后，我们给出一个示例来支持我们的理论结果。
{"title":"Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces","authors":"Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, M. M. Al-Sawalha, Khudhayr A. Rashedi","doi":"10.3390/fractalfract8050289","DOIUrl":"https://doi.org/10.3390/fractalfract8050289","url":null,"abstract":"The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140981942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-13DOI: 10.3390/fractalfract8050288
Shitan Ning, Peng Xia, Fang Hao, Jinqiang Tian, Yong Fu, Ke Wang
Marine shales from the Niutitang Formation and marine–continental transitional shales from the Longtan Formation are two sets of extremely important hydrocarbon source rocks in South China. In order to quantitatively compare the pore complexity characteristics between marine and marine–continental transitional shales, the shale and kerogen of the Niutitang Formation and the Longtan Formation are taken as our research subjects. Based on organic petrology, geochemistry, and low-temperature gas adsorption analyses, the fractal dimension of their pores is calculated by the Frenkel–Halsey–Hill (FHH) and Sierpinski models, and the influences of total organic carbon (TOC), vitrinite reflectance (Ro), and mineral composition on the pore fractals of the shale and kerogen are discussed. Our results show the following: (1) Marine shale predominantly has wedge-shaped and slit pores, while marine–continental transitional shale has inkpot-shaped and slit pores. (2) Cylindrical pores are common in organic matter of both shale types, with marine shale having a greater gas storage space (CRV) from organic matter pores, while marine–continental transitional shale relies more on inorganic pores, especially interlayer clay mineral pores, for gas storage due to their large specific surface area and high adsorption capacity (CRA). (3) The fractal characteristics of marine and marine–continental transitional shale pores are influenced differently. In marine shale, TOC positively correlates with fractal dimensions, while in marine–continental shale, Ro and clay minerals have a stronger influence. Ro is the primary factor affecting organic matter pore complexity. (4) Our two pore fractal models show that the complexity of the shale in the Longtan Formation surpasses that of the shale in the Niutitang Formation, and type I kerogen has more complex organic matter pores than type III, aiding in evaluating pore connectivity and flow effectiveness in shale reservoirs.
{"title":"Pore Fractal Characteristics between Marine and Marine–Continental Transitional Black Shales: A Case Study of Niutitang Formation and Longtan Formation","authors":"Shitan Ning, Peng Xia, Fang Hao, Jinqiang Tian, Yong Fu, Ke Wang","doi":"10.3390/fractalfract8050288","DOIUrl":"https://doi.org/10.3390/fractalfract8050288","url":null,"abstract":"Marine shales from the Niutitang Formation and marine–continental transitional shales from the Longtan Formation are two sets of extremely important hydrocarbon source rocks in South China. In order to quantitatively compare the pore complexity characteristics between marine and marine–continental transitional shales, the shale and kerogen of the Niutitang Formation and the Longtan Formation are taken as our research subjects. Based on organic petrology, geochemistry, and low-temperature gas adsorption analyses, the fractal dimension of their pores is calculated by the Frenkel–Halsey–Hill (FHH) and Sierpinski models, and the influences of total organic carbon (TOC), vitrinite reflectance (Ro), and mineral composition on the pore fractals of the shale and kerogen are discussed. Our results show the following: (1) Marine shale predominantly has wedge-shaped and slit pores, while marine–continental transitional shale has inkpot-shaped and slit pores. (2) Cylindrical pores are common in organic matter of both shale types, with marine shale having a greater gas storage space (CRV) from organic matter pores, while marine–continental transitional shale relies more on inorganic pores, especially interlayer clay mineral pores, for gas storage due to their large specific surface area and high adsorption capacity (CRA). (3) The fractal characteristics of marine and marine–continental transitional shale pores are influenced differently. In marine shale, TOC positively correlates with fractal dimensions, while in marine–continental shale, Ro and clay minerals have a stronger influence. Ro is the primary factor affecting organic matter pore complexity. (4) Our two pore fractal models show that the complexity of the shale in the Longtan Formation surpasses that of the shale in the Niutitang Formation, and type I kerogen has more complex organic matter pores than type III, aiding in evaluating pore connectivity and flow effectiveness in shale reservoirs.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140984577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-11DOI: 10.3390/fractalfract8050287
Minyue He, Huiqi Wang, Lifeng Lin
In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.
{"title":"Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations","authors":"Minyue He, Huiqi Wang, Lifeng Lin","doi":"10.3390/fractalfract8050287","DOIUrl":"https://doi.org/10.3390/fractalfract8050287","url":null,"abstract":"In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140988385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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