Pub Date : 2023-10-14DOI: 10.1142/s0218348x23401928
Zhao Li
In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.
{"title":"Bifurcation, phase portrait, chaotic pattern and traveling wave solution of the fractional perturbed Chen-Lee-Liu model with beta time-space derivative in fiber optics","authors":"Zhao Li","doi":"10.1142/s0218348x23401928","DOIUrl":"https://doi.org/10.1142/s0218348x23401928","url":null,"abstract":"In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"219 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-14DOI: 10.1142/s0218348x23501104
Kang-Le Wang
The Calogero–Bogoyavlenskii–Schiff equation is an important nonlinear evolution model to describe the propagation of Riemann waves. A fractional Calogero–Bogoyavlenskii–Schiff is described based on the conformable derivative for the first time. Some new soliton solutions are acquired with the aid of the extended fractional [Formula: see text] function method and fractional variable method. The two novel mathematical methods are very efficient and concise, which can also be utilized to solve other fractional evolution equations. Furthermore, these derived soliton solutions are illustrated by some 3D and 2D graphs with different fractal parameters and fractal dimensions, which might be helpful to study in plasma physics.
{"title":"New promising and challenges of the fractional Calogero-Bogoyavlenskii-Schiff equation","authors":"Kang-Le Wang","doi":"10.1142/s0218348x23501104","DOIUrl":"https://doi.org/10.1142/s0218348x23501104","url":null,"abstract":"The Calogero–Bogoyavlenskii–Schiff equation is an important nonlinear evolution model to describe the propagation of Riemann waves. A fractional Calogero–Bogoyavlenskii–Schiff is described based on the conformable derivative for the first time. Some new soliton solutions are acquired with the aid of the extended fractional [Formula: see text] function method and fractional variable method. The two novel mathematical methods are very efficient and concise, which can also be utilized to solve other fractional evolution equations. Furthermore, these derived soliton solutions are illustrated by some 3D and 2D graphs with different fractal parameters and fractal dimensions, which might be helpful to study in plasma physics.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we explore the dynamics of quantum correlations in an isolated physical quantum under the influence of intrinsic coherence. We characterize the quantum correlations in the hybrid system using the granular model to investigate the amount of coherent-chaotic fractions, and we particularly use the spherical droplets to measure the specific correlations. Likewise, we examine the effect of coherence on the source evolution of these quantifiers within engineering applications. In particular, the behavior of the multiparticle correlations in terms of the system parameters and the coherence rate is investigated and analyzed in detail to explore the source intrinsic dimensions. We found that the correlations with genuine interferences behave slightly unsymmetrical for identical parameters characterizing the considered complex system and that the genuine correlations are more meaningful than primary interference which probed the chaotic peculiarities against the coherence phenomena. Our results also show that the robustness of quantum correlations can be modulated by adjusting the coherent rate, source physical properties and the initial conditions.
{"title":"Advances in Systems Evolution Through Quantum Correlations within Engineering Applications","authors":"Ghulam Bary, Waqar Ahmed, Riaz Ahmad, Abha Singh, Sayed M. Eldin, Duohui Huang, Ilyas Khan","doi":"10.1142/s0218348x23401874","DOIUrl":"https://doi.org/10.1142/s0218348x23401874","url":null,"abstract":"In this paper, we explore the dynamics of quantum correlations in an isolated physical quantum under the influence of intrinsic coherence. We characterize the quantum correlations in the hybrid system using the granular model to investigate the amount of coherent-chaotic fractions, and we particularly use the spherical droplets to measure the specific correlations. Likewise, we examine the effect of coherence on the source evolution of these quantifiers within engineering applications. In particular, the behavior of the multiparticle correlations in terms of the system parameters and the coherence rate is investigated and analyzed in detail to explore the source intrinsic dimensions. We found that the correlations with genuine interferences behave slightly unsymmetrical for identical parameters characterizing the considered complex system and that the genuine correlations are more meaningful than primary interference which probed the chaotic peculiarities against the coherence phenomena. Our results also show that the robustness of quantum correlations can be modulated by adjusting the coherent rate, source physical properties and the initial conditions.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1142/s0218348x23501189
Q. Zhang, L. J. Lu
In this paper, we have explored the local structure and fractal characteristics of fractal functions with certain fractal dimensions. The conclusion that points with inconsistent oscillation amplitudes with the upper Box dimension of the corresponding fractal functions have been proved to be nowhere dense. This will play an important supporting role in exploring the fractal dimension estimation of the combination of fractal functions.
{"title":"REMARKS ON THE LOCAL STRUCTURE OF REGULAR FRACTAL FUNCTIONS WITH FRACTAL DIMENSIONS","authors":"Q. Zhang, L. J. Lu","doi":"10.1142/s0218348x23501189","DOIUrl":"https://doi.org/10.1142/s0218348x23501189","url":null,"abstract":"In this paper, we have explored the local structure and fractal characteristics of fractal functions with certain fractal dimensions. The conclusion that points with inconsistent oscillation amplitudes with the upper Box dimension of the corresponding fractal functions have been proved to be nowhere dense. This will play an important supporting role in exploring the fractal dimension estimation of the combination of fractal functions.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135922848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1142/s0218348x23501244
NAJMEH PAKNIYAT, BALAMURALI RAMAKRISHNAN, V. PALLAVI, ONDREJ KREJCAR, ROBERT FRISCHER, HAMIDREZA NAMAZI
Analysis of brain activity for patients with brain disorders is an important research area. Mild cognitive impairment (MCI) is a condition in which patients have more memory or thinking problems compared to healthy people of the same age. In this work, we studied the alterations in brain activity among control subjects and patients with MCI. Three complexity techniques, namely sample entropy, approximate entropy, and fractal dimension, were employed to study electroencephalogram (EEG) signals recorded from 102 control (healthy) subjects, and seven subjects with MCI in a comfortable position, on a bed, with their eyes closed. The results showed that the EEG signals of patients with MCI show greater complexity than the EEG signals of healthy subjects. This analysis method can be applied to compare brain activity among healthy subjects and patients with other brain diseases.
{"title":"INVESTIGATING THE VARIATIONS IN THE BRAIN ACTIVITY BETWEEN HEALTHY SUBJECTS AND MILD COGNITIVE IMPAIRMENT (MCI) PATIENTS","authors":"NAJMEH PAKNIYAT, BALAMURALI RAMAKRISHNAN, V. PALLAVI, ONDREJ KREJCAR, ROBERT FRISCHER, HAMIDREZA NAMAZI","doi":"10.1142/s0218348x23501244","DOIUrl":"https://doi.org/10.1142/s0218348x23501244","url":null,"abstract":"Analysis of brain activity for patients with brain disorders is an important research area. Mild cognitive impairment (MCI) is a condition in which patients have more memory or thinking problems compared to healthy people of the same age. In this work, we studied the alterations in brain activity among control subjects and patients with MCI. Three complexity techniques, namely sample entropy, approximate entropy, and fractal dimension, were employed to study electroencephalogram (EEG) signals recorded from 102 control (healthy) subjects, and seven subjects with MCI in a comfortable position, on a bed, with their eyes closed. The results showed that the EEG signals of patients with MCI show greater complexity than the EEG signals of healthy subjects. This analysis method can be applied to compare brain activity among healthy subjects and patients with other brain diseases.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136214040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1142/s0218348x23501128
Ji Ming, Liu Guannan, Yu Boming, Liu Hu, Cheng Gaojie
Concrete is an important part of submarine building structure, which is eroded by hydrostatic pressure and chloride ion. In this study, concrete is regarded as a dually-porous structure composed of pores and fractures. Considering hydrostatic pressure and fractal characteristics of concrete structure, a fractal model is established for chloride ion diffusion under the dual drive of concentration and pressure. Considering the effective stress caused by water pressure in pores of concrete, a fluid–solid model for chloride ion migration is proposed. The fluid–solid coupling fractal model for chloride ion migration was verified by comparing with the experimental data. The numerical simulation results show that: (1) the influence of fractal dimension on the chloride ion diffusion coefficient and chloride ion concentration is nonlinear; (2) compared with low hydrostatic pressure, high hydrostatic pressure has more significant effects on chloride ion concentration and diffusion coefficient; (3) when the effective stress and water pressure in pores are not considered, the diffusion coefficient of chloride ion is always a constant.
{"title":"Simulation of chloride ion transport and erosion in fractal porous media under multi field coupling","authors":"Ji Ming, Liu Guannan, Yu Boming, Liu Hu, Cheng Gaojie","doi":"10.1142/s0218348x23501128","DOIUrl":"https://doi.org/10.1142/s0218348x23501128","url":null,"abstract":"Concrete is an important part of submarine building structure, which is eroded by hydrostatic pressure and chloride ion. In this study, concrete is regarded as a dually-porous structure composed of pores and fractures. Considering hydrostatic pressure and fractal characteristics of concrete structure, a fractal model is established for chloride ion diffusion under the dual drive of concentration and pressure. Considering the effective stress caused by water pressure in pores of concrete, a fluid–solid model for chloride ion migration is proposed. The fluid–solid coupling fractal model for chloride ion migration was verified by comparing with the experimental data. The numerical simulation results show that: (1) the influence of fractal dimension on the chloride ion diffusion coefficient and chloride ion concentration is nonlinear; (2) compared with low hydrostatic pressure, high hydrostatic pressure has more significant effects on chloride ion concentration and diffusion coefficient; (3) when the effective stress and water pressure in pores are not considered, the diffusion coefficient of chloride ion is always a constant.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1142/s0218348x24400085
T. M. C. Priyanka, C. Serpa, A. Gowrisankar
{"title":"α-fractal function with variable parameters: An explicit representation","authors":"T. M. C. Priyanka, C. Serpa, A. Gowrisankar","doi":"10.1142/s0218348x24400085","DOIUrl":"https://doi.org/10.1142/s0218348x24400085","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"220 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135132585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-18DOI: 10.1142/s0218348x24400152
Hasib Khan, Muhammad Aslam, Altaf Hussain Rajpar, Yu-Ming Chu, Sina Etemad, Shahram Rezapour, Hijaz Ahmad
{"title":"A New Fractal-Fractional Hybrid Model for Studying Climate Change on Coastal Ecosystems from the Mathematical Point of View","authors":"Hasib Khan, Muhammad Aslam, Altaf Hussain Rajpar, Yu-Ming Chu, Sina Etemad, Shahram Rezapour, Hijaz Ahmad","doi":"10.1142/s0218348x24400152","DOIUrl":"https://doi.org/10.1142/s0218348x24400152","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135209367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-18DOI: 10.1142/s0218348x24400097
Lu-Chuan Ceng, Boling Chen, Shanli Liao, Van Thien Nguyen, Jen-Chih Yao
{"title":"Solvability and Optimal Control of a System of Semilinear Nonlocal Fractional Evolution Inclusions with Partial Clarke Subdifferential","authors":"Lu-Chuan Ceng, Boling Chen, Shanli Liao, Van Thien Nguyen, Jen-Chih Yao","doi":"10.1142/s0218348x24400097","DOIUrl":"https://doi.org/10.1142/s0218348x24400097","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135209355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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