Pub Date : 2024-08-09DOI: 10.1142/s0218348x24400486
Jagdev Singh, V. Dubey, Devendra Kumar, S. Dubey, Mohammad Sajid
{"title":"A Novel Hybrid Approach for Local Fractional Landau-Ginzburg-Higgs Equation Describing Fractal Heat Flow in Superconductors","authors":"Jagdev Singh, V. Dubey, Devendra Kumar, S. Dubey, Mohammad Sajid","doi":"10.1142/s0218348x24400486","DOIUrl":"https://doi.org/10.1142/s0218348x24400486","url":null,"abstract":"","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"16 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141925331","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 : 2024-04-09DOI: 10.1142/s0218348x24500749
Leonardo H. S. Fernandes, Fernando H. A. Araujo, J. W. Silva, Jose P. V. Fernandes, Urbanno P. S. Leite, Lucas M. Muniz, Ranilson O. A. Paiva, Ibsen M. B. S. Pinto, B. Tabak
{"title":"Spillover Effects of COVID-19 on USA Education Group Stocks","authors":"Leonardo H. S. Fernandes, Fernando H. A. Araujo, J. W. Silva, Jose P. V. Fernandes, Urbanno P. S. Leite, Lucas M. Muniz, Ranilson O. A. Paiva, Ibsen M. B. S. Pinto, B. Tabak","doi":"10.1142/s0218348x24500749","DOIUrl":"https://doi.org/10.1142/s0218348x24500749","url":null,"abstract":"","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"77 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140726504","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}
{"title":"Relative permeability model of two-phase flow in rough capillary rock media based on fractal theory","authors":"Shanshan Yang, Shuaiyin Chen, Xianbao Yuan, Mingqing Zou, Qian Zheng","doi":"10.1142/s0218348x24500750","DOIUrl":"https://doi.org/10.1142/s0218348x24500750","url":null,"abstract":"","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"13 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140722886","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 : 2024-01-23DOI: 10.1142/s0218348x24500282
Yiqi Yao, Caimin Du, Lifeng Xi
The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov’s idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044] to figure out the exact formula of edge-Wiener index of the Sierpinski fractal networks.
边-维纳指数是表示图中每对边之间距离总和的不变指数，在化学和材料科学研究中具有重要影响。本文从格罗莫夫的思想中得到启发，利用王晓东等人提出的有限模式法[Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044]，算出了Sierpinski分形网络的边-维纳指数的精确公式。
{"title":"EDGE-WIENER INDEX OF SIERPINSKI FRACTAL NETWORKS","authors":"Yiqi Yao, Caimin Du, Lifeng Xi","doi":"10.1142/s0218348x24500282","DOIUrl":"https://doi.org/10.1142/s0218348x24500282","url":null,"abstract":"The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov’s idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044] to figure out the exact formula of edge-Wiener index of the Sierpinski fractal networks.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"5 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604437","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 : 2024-01-23DOI: 10.1142/s0218348x24500269
Kang-Jia Wang, Feng Shi
The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the [Formula: see text] and [Formula: see text] functions that are derived on the basis of the Mittag-Leffler function (MLF) defined on the Cantor set (CS), are employed to construct the auxiliary trial function to look into the exact solutions (ESs). Aided by Yang’s non-differentiable (ND) transformation, six groups of the ND ESs are found. The ND ESs on the CS for [Formula: see text] are depicted graphically. Additionally, as a comparison, the ESs of the classic (3+1)-dimensional MZKe for [Formula: see text] are also illustrated. The outcomes reveal that the derived method is powerful and effective, and can be used to deal with the other local fractional PDEs.
{"title":"A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION","authors":"Kang-Jia Wang, Feng Shi","doi":"10.1142/s0218348x24500269","DOIUrl":"https://doi.org/10.1142/s0218348x24500269","url":null,"abstract":"The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the [Formula: see text] and [Formula: see text] functions that are derived on the basis of the Mittag-Leffler function (MLF) defined on the Cantor set (CS), are employed to construct the auxiliary trial function to look into the exact solutions (ESs). Aided by Yang’s non-differentiable (ND) transformation, six groups of the ND ESs are found. The ND ESs on the CS for [Formula: see text] are depicted graphically. Additionally, as a comparison, the ESs of the classic (3+1)-dimensional MZKe for [Formula: see text] are also illustrated. The outcomes reveal that the derived method is powerful and effective, and can be used to deal with the other local fractional PDEs.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"34 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603242","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 : 2024-01-23DOI: 10.1142/s0218348x24500270
Ju-Hong Lu
This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.
本文重点对 (3+1) 维势能-Yu-Toda-Sasa-Fukuyama（YTSF）方程的分形修正进行数值研究。本文提出了一种基于二尺度分形复变和变分原理的变分方法来求解该分形方程。分形势-YTSF 方程可以通过分形复变转换为原始势-YTSF 方程。利用贺建奎提出的变分原理，提供了一些分形孤子型解法和分形周期波解法，这在现有文献中是没有的。此外，还对 Manafian 等人[East Asian J. Appl.给出了不同分形维数和振幅的分形波解的数值结果，以显示其传播行为。
{"title":"APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION","authors":"Ju-Hong Lu","doi":"10.1142/s0218348x24500270","DOIUrl":"https://doi.org/10.1142/s0218348x24500270","url":null,"abstract":"This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603912","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 : 2024-01-23DOI: 10.1142/s0218348x24500294
Joel Ratsaby
Consider orbits [Formula: see text] of the fractal iterator [Formula: see text], [Formula: see text], that start at initial points [Formula: see text], where [Formula: see text] is the set of all rational complex numbers (their real and imaginary parts are rational) and [Formula: see text] consists of all such [Formula: see text] whose complexity does not exceed some complexity parameter value [Formula: see text] (the complexity of [Formula: see text] is defined as the number of bits that suffice to describe the real and imaginary parts of [Formula: see text] in lowest form). The set [Formula: see text] is a bounded-complexity approximation of the filled Julia set [Formula: see text]. We present a new perspective on fractals based on an analogy with Chaitin’s algorithmic information theory, where a rational complex number [Formula: see text] is the analog of a program [Formula: see text], an iterator [Formula: see text] is analogous to a universal Turing machine [Formula: see text] which executes program [Formula: see text], and an unbounded orbit [Formula: see text] is analogous to an execution of a program [Formula: see text] on [Formula: see text] that halts. We define a real number [Formula: see text] which resembles Chaitin’s [Formula: see text] number, where, instead of being based on all programs [Formula: see text] whose execution on [Formula: see text] halts, it is based on all rational complex numbers [Formula: see text] whose orbits under [Formula: see text] are unbounded. Hence, similar to Chaitin’s [Formula: see text] number, [Formula: see text] acts as a theoretical limit or a “fractal oracle number” that provides an arbitrarily accurate complexity-based approximation of the filled Julia set [Formula: see text]. We present a procedure that, when given [Formula: see text] and [Formula: see text], it uses [Formula: see text] to generate [Formula: see text]. Several numerical examples of sets that estimate [Formula: see text] are presented.
{"title":"FRACTAL ORACLE NUMBERS","authors":"Joel Ratsaby","doi":"10.1142/s0218348x24500294","DOIUrl":"https://doi.org/10.1142/s0218348x24500294","url":null,"abstract":"Consider orbits [Formula: see text] of the fractal iterator [Formula: see text], [Formula: see text], that start at initial points [Formula: see text], where [Formula: see text] is the set of all rational complex numbers (their real and imaginary parts are rational) and [Formula: see text] consists of all such [Formula: see text] whose complexity does not exceed some complexity parameter value [Formula: see text] (the complexity of [Formula: see text] is defined as the number of bits that suffice to describe the real and imaginary parts of [Formula: see text] in lowest form). The set [Formula: see text] is a bounded-complexity approximation of the filled Julia set [Formula: see text]. We present a new perspective on fractals based on an analogy with Chaitin’s algorithmic information theory, where a rational complex number [Formula: see text] is the analog of a program [Formula: see text], an iterator [Formula: see text] is analogous to a universal Turing machine [Formula: see text] which executes program [Formula: see text], and an unbounded orbit [Formula: see text] is analogous to an execution of a program [Formula: see text] on [Formula: see text] that halts. We define a real number [Formula: see text] which resembles Chaitin’s [Formula: see text] number, where, instead of being based on all programs [Formula: see text] whose execution on [Formula: see text] halts, it is based on all rational complex numbers [Formula: see text] whose orbits under [Formula: see text] are unbounded. Hence, similar to Chaitin’s [Formula: see text] number, [Formula: see text] acts as a theoretical limit or a “fractal oracle number” that provides an arbitrarily accurate complexity-based approximation of the filled Julia set [Formula: see text]. We present a procedure that, when given [Formula: see text] and [Formula: see text], it uses [Formula: see text] to generate [Formula: see text]. Several numerical examples of sets that estimate [Formula: see text] are presented.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"130 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604938","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 : 2024-01-23DOI: 10.1142/s0218348x24500245
Kang-Jia Wang, JING-HUA Liu, Feng Shi
The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale transform is employed to investigate the other soliton solutions, which include the kink soliton and the rough wave soliton solutions. The impact of the different fractal orders on the physical behaviors of the semi-domain soliton solutions is also discussed graphically. The methods mentioned in this research are expected to provide some new viewpoints on the behaviors of the fractal PDEs.
{"title":"ON THE SEMI-DOMAIN SOLITON SOLUTIONS FOR THE FRACTAL (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI– BOUSSINESQ EQUATION","authors":"Kang-Jia Wang, JING-HUA Liu, Feng Shi","doi":"10.1142/s0218348x24500245","DOIUrl":"https://doi.org/10.1142/s0218348x24500245","url":null,"abstract":"The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale transform is employed to investigate the other soliton solutions, which include the kink soliton and the rough wave soliton solutions. The impact of the different fractal orders on the physical behaviors of the semi-domain soliton solutions is also discussed graphically. The methods mentioned in this research are expected to provide some new viewpoints on the behaviors of the fractal PDEs.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"23 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603076","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 : 2024-01-18DOI: 10.1142/s0218348x2450021x
Jiajun Xu, Lifeng Xi
The hyper-Wiener index plays an important role in chemical graph theory. In this paper, using the technique named finite pattern, we discuss the hyper-Wiener index on level-3 Sierpinski gasket which is a self-similar fractal.
{"title":"HYPER-WIENER INDEX ON LEVEL-3 SIERPINSKI GASKET","authors":"Jiajun Xu, Lifeng Xi","doi":"10.1142/s0218348x2450021x","DOIUrl":"https://doi.org/10.1142/s0218348x2450021x","url":null,"abstract":"The hyper-Wiener index plays an important role in chemical graph theory. In this paper, using the technique named finite pattern, we discuss the hyper-Wiener index on level-3 Sierpinski gasket which is a self-similar fractal.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"119 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139614026","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 : 2024-01-18DOI: 10.1142/s0218348x24500130
QIAN-RUI Zhong, HONG-YONG Wang
In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by changes of weights. Finally, we give their box dimension estimates for a specific type of the FISs.
{"title":"CONSTRUCTION OF A WEIGHTED FRACTAL INTERPOLATION SURFACE BASED ON MATKOWSKI CONTRACTIONS","authors":"QIAN-RUI Zhong, HONG-YONG Wang","doi":"10.1142/s0218348x24500130","DOIUrl":"https://doi.org/10.1142/s0218348x24500130","url":null,"abstract":"In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by changes of weights. Finally, we give their box dimension estimates for a specific type of the FISs.","PeriodicalId":502452,"journal":{"name":"Fractals","volume":"106 49","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139614608","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}
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