Fractals最新文献

{"title":"NEW FRACTIONAL INTEGRAL INEQUALITIES FORLR-ℏ-PREINVEX INTERVAL-VALUED FUNCTIONS","authors":"YUN TAN, DAFANG ZHAO","doi":"10.1142/s0218348x2450083x","DOIUrl":"https://doi.org/10.1142/s0218348x2450083x","url":null,"abstract":"<p>Based on the pseudo-order relation, we introduce the concept of left and right <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>ℏ</mi></math></span><span></span>-preinvex interval-valued functions (LR-<span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>ℏ</mi></math></span><span></span>-PIVFs). Further, we establish the Hermite–Hadamard and Hermite–Hadamard–Fejér-type estimates for LR-<span><math altimg=\"eq-00005.gif\" display=\"inline\"><mi>ℏ</mi></math></span><span></span>-PIVFs using generalized fractional integrals. Finally, an example of interval-valued fractional integrals is provided to illustrate the validity of the results derived herein. Our results not only extend some existing inequalities for Hadamard, Riemann–Liouville, and Katugampola fractional integrals, but also provide new insights for future research on generalized convexity and IVFs, among others.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182632","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":"A MODERN TRAVELING WAVE SOLUTION FOR CAPUTO-FRACTIONAL KLEIN–GORDON EQUATIONS","authors":"AHMAD EL-AJOU, RANIA SAADEH, ALIAA BURQAN, MAHMOUD ABDEL-ATY","doi":"10.1142/s0218348x24500841","DOIUrl":"https://doi.org/10.1142/s0218348x24500841","url":null,"abstract":"<p>This research paper introduces a novel approach to deriving traveling wave solutions (TWSs) for the Caputo-fractional Klein–Gordon equations. This research presents a distinct methodological advancement by introducing TWSs of a particular time-fractional partial differential equation, utilizing a non-local fractional operator, specifically the Caputo derivative. To achieve our goal, a novel transformation is considered, that converts a time-fractional partial differential equation into fractional ordinary differential equations, enabling analytical solutions through various analytical methods. This paper employs the homotopy analysis method to achieve the target objectives. To demonstrate the efficiency and applicability of the proposed transform and method, two examples are discussed and analyzed in figures.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182622","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":"QUANTIFYING ROUGH FRACTURE BEHAVIORS IN GAS-BEARING COAL SEAM: A FULLY COUPLED FRACTAL ANALYSIS","authors":"ZHOU ZHOU, WAN ZHIJUN, LIU GUANNAN, YU BOMING, YE DAYU, WEI MINGYAO","doi":"10.1142/s0218348x24500853","DOIUrl":"https://doi.org/10.1142/s0218348x24500853","url":null,"abstract":"<p>In gas-bearing coal seam mining projects, the pivotal considerations encompass the assessment of gas migration, emission trends, and coal seam stability, which are crucial for ensuring both the safety and efficiency of the project. The accurate evaluation of the nonlinear evolution of the fracture network, acting as the primary conduit for gas migration and influenced by mining disturbances, coal seam stress, overlying strata pressure, and gas pressure, emerges as a key determinant in gauging coal seam stress and safety. To address the industry challenge of quantitatively assessing the complex behaviors of fracture networks during gas-bearing coal seam extraction, this study introduces a novel, interdisciplinary fractal analysis model. Drawing upon fractal theory for classical porous media, four fractal parameters capable of quantitatively characterizing the microscopic behaviors of fractures are proposed and defined as functions of permeability. Subsequently, the gas pressure in gas-bearing coal seams, coal seam deformation and stress, in-situ stress, overlying strata pressure, and adsorption–desorption effects are comprehensively coupled and applied to the classic gas-bearing coal seam at the Jianxin Coal Mine’s 4301 working face in Shaanxi, China. Upon the robust validation of the proposed model, the present computational results reveal: (1) the proposed micro-parameters adeptly characterize the number, roughness, tortuosity, and length of fractures in gas-bearing coal seams; (2) a larger fractal dimension of fractures leads to increased coal seam stress and strain, while the fractal dimensions of fracture tortuosity and roughness are inversely proportional to coal seam stress and strain; (3) these fractal parameters directly induce evolutionary changes in gas seepage behavior, leading to varying degrees of mechanical property evolution in the coal seam. When <span><math altimg=\"eq-00001.gif\" display=\"inline\"><msub><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span><span></span> and <span><math altimg=\"eq-00002.gif\" display=\"inline\"><msub><mrow><mi>D</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span><span></span> increased from 1.2 to 1.8, the maximum change in coal seam deformation was 16.9% and 13.8%, respectively, and when <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>𝜀</mi></math></span><span></span> increases from 0.03 to 0.12, the coal seam deformation changes by 15.1%. This represents a quantitative characterization unattainable by previously published coal seam analysis models, including mainstream fractal computation models.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182673","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":"Dynamics of optical wave profiles to the fractional three-component coupled nonlinear Schrodinger equation","authors":"Usman Younas, Tukur A. Sulaiman, Qasim Ali, A. Majeed, Krzystof Kedzia, Ahmed Z. Jan","doi":"10.1142/s0218348x24500865","DOIUrl":"https://doi.org/10.1142/s0218348x24500865","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141106409","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":"VARIATIONAL PRINCIPLE FOR A FRACTAL LUBRICATION PROBLEM","authors":"YU-TING ZUO","doi":"10.1142/s0218348x24500804","DOIUrl":"https://doi.org/10.1142/s0218348x24500804","url":null,"abstract":"<p>Micro/nanoscale lubrication must take into account the fractal profile of the shaft and bearing surfaces. A new fractal rheological model is proposed to describe the properties of the non-Newtonian fluid, and a fractal variational principle is established by the semi-inverse method, and finally the Lagrange multipliers can be found in the obtained variational formulation. This work provides a new fractal approach to nano/micro lubrication.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156655","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":"THE FRACTAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION: GENERALIZED VARIATIONAL PRINCIPLE AND THE SEMI-DOMAIN SOLUTIONS","authors":"KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XU","doi":"10.1142/s0218348x24500798","DOIUrl":"https://doi.org/10.1142/s0218348x24500798","url":null,"abstract":"<p>By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions are also explored by applying the variational approach and the one-step method namely Wang’s direct mapping method-II. The dynamics of the extracted solutions on the Cantor set are unveiled graphically. The findings of this study are expected to provide some new insights into the exploration of the fractal PDEs.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156672","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":"Complexity-based analysis of the variations in the brain response of porn-addicted and healthy individuals under different function tasks","authors":"Najmeh Pakniyat, Janarthanan Ramadoss, Anitha Karthikeyan, Penhaker Marek, Ondrej Krejcar, Hamidreza Namazi","doi":"10.1142/s0218348x24500907","DOIUrl":"https://doi.org/10.1142/s0218348x24500907","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"39 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141107723","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":"The fractal rheology of magnetorheological elastomers described through the modified Zener model and the Cole-Cole plot","authors":"Luis M. Palacios-Pineda, Alex Elias-Zuniga, I. A. Perales-Martinez, Oscar Martinez-Romero, Daniel Olvera-Trejo","doi":"10.1142/s0218348x24500877","DOIUrl":"https://doi.org/10.1142/s0218348x24500877","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"14 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141104784","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":"Generalized rings around sierpinski holes","authors":"Sinhyok Pak, Hyegyong Jang","doi":"10.1142/s0218348x24500889","DOIUrl":"https://doi.org/10.1142/s0218348x24500889","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"12 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141107593","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":"Detection and characterization of cusp singularities","authors":"Selin Buyuktas, Deniz Karacor","doi":"10.1142/s0218348x24500890","DOIUrl":"https://doi.org/10.1142/s0218348x24500890","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"12 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141105602","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}