Pub Date : 2024-07-03DOI: 10.1142/s0218348x24501056
Yiqun Sun, Jianming Qi, Qinghua Cui
{"title":"Analyzing the occurrence of bifurcation and chaotic behaviors in multi-fractional order stochastic Ginzburg-Landau equations","authors":"Yiqun Sun, Jianming Qi, Qinghua Cui","doi":"10.1142/s0218348x24501056","DOIUrl":"https://doi.org/10.1142/s0218348x24501056","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"81 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682650","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: 10.1142/s0218348x2450107x
Yuanyuan Li, Lihui Tu
{"title":"Weighted Average Distance of the Self-Similar Coral Fractal","authors":"Yuanyuan Li, Lihui Tu","doi":"10.1142/s0218348x2450107x","DOIUrl":"https://doi.org/10.1142/s0218348x2450107x","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"17 S2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681555","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":"Temporal evolution of permeability for porous rock during mineral dissolution and precipitation process based on fractal theory","authors":"Aimin Chen, Tongjun Miao, Xiaomeng Shen, Boming Yu","doi":"10.1142/s0218348x24501020","DOIUrl":"https://doi.org/10.1142/s0218348x24501020","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"40 S184","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683200","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: 10.1142/s0218348x24501044
J. R. Guo, Y. S. Liang
{"title":"On the fractal dimension of a fractal surface with one single unbounded variation point","authors":"J. R. Guo, Y. S. Liang","doi":"10.1142/s0218348x24501044","DOIUrl":"https://doi.org/10.1142/s0218348x24501044","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"7 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683439","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: 10.1142/s0218348x24500920
Yu-Ting Zuo
Tree-like branching networks are widespread in nature and have found wide applications in engineering, where Murray’s law is generally adopted to optimally design tree-like systems, but it may become invalid in some cases. Here we give an energy approach to the analysis of the law and re-find Li–Yu’s law for the optimal ratio of the square root of 2 with a suitable constraint. When the cross-section of each branch is considered as a fractal pattern, a modified Murray’s law is obtained, which includes the original Murray’s law for a Peano-like pore and Li–Yu’s law for cylindrical branches, furthermore a useful relationship between the diameter and length of each hierarchy is obtained, which is contrary to the tree-like fractal patterns, and the new hierarchy is named as “fractal Murray tree”, which also has many potential applications in science, engineering, social science and economics. This paper is intended to serve as a foundation for further research into the fractal Murray tree and its applications in various fields.
{"title":"ON MURRAY LAW FOR OPTIMAL BRANCHING RATIO","authors":"Yu-Ting Zuo","doi":"10.1142/s0218348x24500920","DOIUrl":"https://doi.org/10.1142/s0218348x24500920","url":null,"abstract":"Tree-like branching networks are widespread in nature and have found wide applications in engineering, where Murray’s law is generally adopted to optimally design tree-like systems, but it may become invalid in some cases. Here we give an energy approach to the analysis of the law and re-find Li–Yu’s law for the optimal ratio of the square root of 2 with a suitable constraint. When the cross-section of each branch is considered as a fractal pattern, a modified Murray’s law is obtained, which includes the original Murray’s law for a Peano-like pore and Li–Yu’s law for cylindrical branches, furthermore a useful relationship between the diameter and length of each hierarchy is obtained, which is contrary to the tree-like fractal patterns, and the new hierarchy is named as “fractal Murray tree”, which also has many potential applications in science, engineering, social science and economics. This paper is intended to serve as a foundation for further research into the fractal Murray tree and its applications in various fields.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"54 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688343","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 : 2024-06-06DOI: 10.1142/s0218348x24400437
Imtiaz Ahmad, Asmidar Abu Bakar, Hijaz Ahmad, Aziz Khan, Th. Abdeljawad
{"title":"Investigating Virus Spread Analysis in Computer Networks with Atangana-Baleanu Fractional Derivative Models","authors":"Imtiaz Ahmad, Asmidar Abu Bakar, Hijaz Ahmad, Aziz Khan, Th. Abdeljawad","doi":"10.1142/s0218348x24400437","DOIUrl":"https://doi.org/10.1142/s0218348x24400437","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"65 s297","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141377215","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: 10.1142/s0218348x24500786
JIANG DENG, JIHUA MA, KUNKUN SONG, ZHONGQUAN XIE
Let be the Lüroth expansion of , and let . It is shown that for any , the level set has Hausdorff dimension one. Certain sets of points for which the sequence grows more rapidly are also investigated.
{"title":"SOME FRACTALS RELATED TO PARTIAL MAXIMAL DIGITS IN LÜROTH EXPANSION","authors":"JIANG DENG, JIHUA MA, KUNKUN SONG, ZHONGQUAN XIE","doi":"10.1142/s0218348x24500786","DOIUrl":"https://doi.org/10.1142/s0218348x24500786","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mo stretchy=\"false\">[</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>,</mo><mo>…</mo><mo stretchy=\"false\">]</mo></math></span><span></span> be the Lüroth expansion of <span><math altimg=\"eq-00002.gif\" display=\"inline\"><mi>x</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">]</mo></math></span><span></span>, and let <span><math altimg=\"eq-00003.gif\" display=\"inline\"><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo>max</mo><mo stretchy=\"false\">{</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">}</mo></math></span><span></span>. It is shown that for any <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>α</mi><mo>≥</mo><mn>0</mn></math></span><span></span>, the level set <disp-formula-group><span><math altimg=\"eq-00005.gif\" display=\"block\"><mrow><mstyle><mfenced close=\"\" open=\"{\" separators=\"\"><mrow></mrow></mfenced></mstyle><mi>x</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">]</mo><mo>:</mo><munder><mrow><mo>lim</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>log</mo><mo>log</mo><mi>n</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mo>=</mo><mi>α</mi><mstyle><mfenced close=\"\" open=\"}\" separators=\"\"><mrow></mrow></mfenced></mstyle></mrow></math></span><span></span></disp-formula-group> has Hausdorff dimension one. Certain sets of points for which the sequence <span><math altimg=\"eq-00006.gif\" display=\"inline\"><msub><mrow><mo stretchy=\"false\">{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math></span><span></span> grows more rapidly are also investigated.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141246524","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":"Study on quantification of rock fracture network to promote shale gas development","authors":"Lili Sui, Xinyu Ma, Jiamin Chen, Xiaodong Wang, Fangping Niu, Jiaqi Tao","doi":"10.1142/s0218348x24400310","DOIUrl":"https://doi.org/10.1142/s0218348x24400310","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"67 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141387442","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 : 2024-05-30DOI: 10.1142/s0218348x24500774
KANG-LE WANG
The primary aim of this work is to investigate the nonlinear fractional Schrödinger equation, which is adopted to describe the ultra-short pulses in optical fibers. A variety of new soliton solutions and periodic solutions are constructed by implementing three efficient mathematical approaches, namely, the improved fractional -expansion method, fractional Bernoulli (/-expansion method and fractional cosine-sine method. Moreover, the dynamic properties of these obtained solutions are discussed by plotting some 3D and 2D figures. The employed three analytical methods can be widely adopted to solve different types of fractional evolution equations.
这项工作的主要目的是研究非线性分数薛定谔方程，该方程用于描述光纤中的超短脉冲。通过采用三种有效的数学方法，即改进的分数 F 展开法、分数伯努利 (G′/G) 展开法和分数余弦正弦法，构建了多种新的孤子解和周期解。此外，还通过绘制一些三维和二维图形讨论了这些求解的动态特性。所采用的三种分析方法可广泛用于求解不同类型的分数演化方程。
{"title":"NEW OPTICAL SOLITONS FOR NONLINEAR FRACTIONAL SCHRÖDINGER EQUATION VIA DIFFERENT ANALYTICAL APPROACHES","authors":"KANG-LE WANG","doi":"10.1142/s0218348x24500774","DOIUrl":"https://doi.org/10.1142/s0218348x24500774","url":null,"abstract":"<p>The primary aim of this work is to investigate the nonlinear fractional Schrödinger equation, which is adopted to describe the ultra-short pulses in optical fibers. A variety of new soliton solutions and periodic solutions are constructed by implementing three efficient mathematical approaches, namely, the improved fractional <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mi>F</mi></math></span><span></span>-expansion method, fractional Bernoulli (<span><math altimg=\"eq-00002.gif\" display=\"inline\"><msup><mrow><mi>G</mi></mrow><mrow><mi>′</mi></mrow></msup></math></span><span></span>/<span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-expansion method and fractional cosine-sine method. Moreover, the dynamic properties of these obtained solutions are discussed by plotting some 3D and 2D figures. The employed three analytical methods can be widely adopted to solve different types of fractional evolution equations.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182665","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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