Fractals最新文献

{"title":"FAST AND ACCURATE POPULATION FORECASTING WITH TWO-SCALE FRACTAL POPULATION DYNAMICS AND ITS APPLICATION TO POPULATION ECONOMICS","authors":"YARONG ZHANG, NAVEED ANJUM, DAN TIAN, ABDULRAHMAN ALI ALSOLAMI","doi":"10.1142/s0218348x24500828","DOIUrl":"https://doi.org/10.1142/s0218348x24500828","url":null,"abstract":"<p>One of the major challenges in population economics is accurately predicting population size. Incorrect predictions can lead to ineffective population control policies. Traditional differential models assume a smooth change in population, but this assumption is invalid when measuring population on a small-time scale. To address this change, we developed two-scale fractal population dynamics that can accurately predict population size with minimal experimental data. The Taylor series method is used to reveal the population’s dynamical properties, and the Padé technology is adopted to accelerate the convergence rate.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156647","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":"MODIFIED SHRINKING TARGET PROBLEM FOR MATRIX TRANSFORMATIONS OF TORI","authors":"NA YUAN, SHUAILING WANG","doi":"10.1142/s0218348x24500762","DOIUrl":"https://doi.org/10.1142/s0218348x24500762","url":null,"abstract":"<p>In this paper, we calculate the Hausdorff dimension of the fractal set <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mfenced close=\"}\" open=\"{\" separators=\"\"><mrow><mstyle mathvariant=\"monospace\"><mi>x</mi></mstyle><mo>∈</mo><msup><mrow><mi>𝕋</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>:</mo><munder><mrow><mo>∏</mo></mrow><mrow><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>d</mi></mrow></munder><mo>|</mo><msubsup><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi>n</mi></mrow></msubsup><mo stretchy=\"false\">(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">−</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>&lt;</mo><mi>ψ</mi><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mtext> </mtext><mstyle><mtext>for infinitely many </mtext></mstyle><mi>n</mi><mo>∈</mo><mi>ℕ</mi></mrow></mfenced><mspace width=\"-.17em\"></mspace><mo>,</mo></mrow></math></span><span></span></disp-formula-group> where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></math></span><span></span> is the standard <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span><span></span>-transformation with <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span><span></span>, <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>ψ</mi></math></span><span></span> is a positive function on <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℕ</mi></math></span><span></span> and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo>|</mo><mo stretchy=\"false\">⋅</mo><mo>|</mo></math></span><span></span> is the usual metric on the torus <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝕋</mi></math></span><span></span>. Moreover, we investigate a modified version of the shrinking target problem, which unifies the shrinking target problems and quantitative recurrence properties for matrix transformations of tori. Let <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>T</mi></math></span><span></span> be a <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>d</mi><mo stretchy=\"false\">×</mo><mi>d</mi></math></span><span></span> non-singular matrix with real coefficients. Then, <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>T</mi></math></span><span></span> determines a self-map of the <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>d</mi></math></span><span></span>-dimensional torus <span><math al","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156606","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":"ON THE PERIODIC SOLITON SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS","authors":"Rashid Ali, Devendra Kumar, A. Akgül, Ali A. Altalbe","doi":"10.1142/s0218348x24400334","DOIUrl":"https://doi.org/10.1142/s0218348x24400334","url":null,"abstract":"In this research, we use a novel version of the Extended Direct Algebraic Method (EDAM) namely generalized EDAM (gEDAM) to investigate periodic soliton solutions for nonlinear systems of fractional Schrödinger equations (FSEs) with conformable fractional derivatives. The FSEs, which is the fractional abstraction of the Schrödinger equation, grasp notable relevance in quantum mechanics. The proposed gEDAM technique entails creating nonlinear ordinary differential equations via a fractional complex transformation, which are then solved to acquire soliton solutions. Several 3D and contour graphs of the soliton solutions reveal periodicity in the wave profiles that offer crucial perspectives into the behavior of the system. The work sheds light on the dynamics of FSEs by displaying numerous families of periodic soliton solutions and their intricate relationships. These results hold significance not only for comprehending the dynamics of FSEs but also for nonlinear fractional partial differential equation applications.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"23 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141118057","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":"DESIGN AND IMPLEMENTATION OF FUZZY-FRACTIONAL WU–ZHANG SYSTEM USING HE–MOHAND ALGORITHM","authors":"MUBASHIR QAYYUM, Efaza Ahmad, MUHAMMAD SOHAIL, NADIA SARHAN, EMAD MAHROUS AWWAD, A. Iqbal","doi":"10.1142/s0218348x24400322","DOIUrl":"https://doi.org/10.1142/s0218348x24400322","url":null,"abstract":"In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended He–Mohand algorithm is proposed for the solution and analysis of the current model. This approach is based on homotopy perturbation method along with Mohand transformation. Effectiveness of proposed methodology at upper and lower bounds is confirmed through residual errors. The theoretical convergence of proposed algorithm is proved alongside numerical computations. Existence and uniqueness of solution are also theoretically proved in the given paper. Current investigation considers three types of fuzzifications i.e. fuzzified equations, fuzzified conditions, and finally fuzzification in both model and conditions. Different physical aspects of WZ system profiles are analyzed through 2D and 3D illustrations at upper and lower bounds. The obtained results highlight the impact of uncertainty on WZ system in fuzzy-fractional space. Hence, the proposed methodology can be used for other fuzzy-fractional systems for better accuracy with lesser computational cost.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"127 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115621","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":"Forecasting the Behaviour of Fractional Model of Emden-Fowler Equation with Caputo-Katugampola Memory","authors":"Jagdev Singh, Arpita Gupta, Juan J. Nieto","doi":"10.1142/s0218348x2440036x","DOIUrl":"https://doi.org/10.1142/s0218348x2440036x","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"77 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122794","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":"Nonlinearity and memory effects: The interplay between these two crucial factors in the Harry Dym model","authors":"Mostafa M. A. Khater, S. H. Alfalqi","doi":"10.1142/s0218348x24400346","DOIUrl":"https://doi.org/10.1142/s0218348x24400346","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"98 51","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122666","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":"On a New α-Convexity with Respect to a Parameter: Applications on the Means and Fractional Inequalities","authors":"M. Samraiz, Tahira Atta, Hossam A. Nabwey, S. Naheed, Sina Etemad","doi":"10.1142/s0218348x24400358","DOIUrl":"https://doi.org/10.1142/s0218348x24400358","url":null,"abstract":"","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"99 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122569","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":"PREFACE — SPECIAL ISSUE ON FRACTALS AND LOCAL FRACTIONAL CALCULUS: RECENT ADVANCES AND FUTURE CHALLENGES","authors":"Xiao-Jun Yang, D. Baleanu, J. A. TENREIRO MACHADO, CARLO CATTANI","doi":"10.1142/s0218348x24020031","DOIUrl":"https://doi.org/10.1142/s0218348x24020031","url":null,"abstract":"Fractal geometry plays an important role in the description of the characteristics of nature. Local fractional calculus, a new branch of mathematics, is used to handle the non-differentiable problems in mathematical physics and engineering sciences. The local fractional inequalities, local fractional ODEs and local fractional PDEs via local fractional calculus are studied. Fractional calculus is also considered to express the fractal behaviors of the functions, which have fractal dimensions. The interesting problems from fractional calculus and fractals are reported. With the scaling law, the scaling-law vector calculus via scaling-law calculus is suggested in detail. Some special functions related to the classical, fractional, and power-law calculus are also presented to express the Kohlrausch–Williams–Watts function, Mittag-Leffler function and Weierstrass–Mandelbrot function. They have a relation to the ODEs, PDEs, fractional ODEs and fractional PDEs in real-world problems. Theory of the scaling-law series via Kohlrausch–Williams–Watts function is suggested to handle real-world problems. The hypothesis for the tempered Xi function is proposed as the Fractals Challenge, which is a new challenge in the field of mathematics. The typical applications of fractal geometry are proposed in real-world problems.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976511","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":"EDGE-WIENER INDEX OF LEVEL-3 SIERPINSKI SKELETON NETWORK","authors":"CAIMIN DU, YIQI YAO, LIFENG XI","doi":"10.1142/s0218348x24500816","DOIUrl":"https://doi.org/10.1142/s0218348x24500816","url":null,"abstract":"<p>The edge-Wiener index is an important topological index in Chemical Graph Theory, defined as the sum of distances among all pairs of edges. Fractal structures have received much attention from scientists because of their philosophical and aesthetic significance, and chemists have even attempted to synthesize various types of molecular fractal structures. The level-3 Sierpinski triangle is constructed similarly to the Sierpinski triangle and its skeleton networks have self-similarity. In this paper, by using the method of finite pattern, we obtain the edge-Wiener index of skeleton networks according to level-3 Sierpinski triangle. This provides insights for a better understanding of molecular fractal structures.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141156638","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":"DISTRIBUTIONAL INVARIANCE IN BINARY MULTIPLICATIVE CASCADES","authors":"CÉSAR AGUILAR-FLORES, ALIN-ANDREI CARSTEANU","doi":"10.1142/s0218348x24500725","DOIUrl":"https://doi.org/10.1142/s0218348x24500725","url":null,"abstract":"<p>The stability properties of certain probability distribution functions under the combined effects of cascading and “dressing” in a binary multiplicative cascade are contemplated and proven herein. Their main importance for applications resides in parameterizing the multiplicative cascade generators of multifractal measures from single realizations, given the generic lack of distributional ergodicity of those cascades. The results are also being illustrated by numerical simulations.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140814450","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}