Computational and Mathematical Methods最新文献

Computational Analysis of a Nonautonomous Incommensurate Fractional-Order Swing System: Chaos, Control, and Image Cryptography 非自治不相称分数阶摆动系统的计算分析：混沌、控制和图像密码

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-10-02 DOI: 10.1155/cmm4/5351460

Sabrina Riah, Adel Ouannas, Giuseppe Grassi, Abdulmajeed Alsubhi, Noureddine Djenina, Imane Zouak

{"title":"Computational Analysis of a Nonautonomous Incommensurate Fractional-Order Swing System: Chaos, Control, and Image Cryptography","authors":"Sabrina Riah, Adel Ouannas, Giuseppe Grassi, Abdulmajeed Alsubhi, Noureddine Djenina, Imane Zouak","doi":"10.1155/cmm4/5351460","DOIUrl":"https://doi.org/10.1155/cmm4/5351460","url":null,"abstract":"In this paper, the dynamic behavior of an incommensurate fractional-order single-machine infinite-bus (IFOSMIB) power system is investigated through numerical simulations. Different dynamical phenomena are observed in the IFOSMIB system, including periodic oscillations, period-doubling bifurcations, and chaotic attractors. Furthermore, the complexity of the system dynamics is quantified using the complexity measure C0. In addition, the positivity of the largest Lyapunov exponent (LLE) and the results of the 0–1 test for chaos, a robust indicator for distinguishing regular dynamics from chaotic dynamics, confirm the existence of chaos in the system. Moreover, an effective control scheme is proposed to suppress the chaotic oscillations of the IFOSMIB power system, and its effectiveness is verified through numerical simulations. Furthermore, the proposed fractional-order chaotic system is investigated for information security applications. Its complex and highly sensitive dynamics are exploited in the development of a chaos-based encryption scheme, in which the generated chaotic sequences are employed for secure data encryption. The obtained results demonstrate the potential of the proposed system for cryptographic and secure communication applications.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/5351460","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computational Analysis of a Nonautonomous Incommensurate Fractional-Order Swing System: Chaos, Control, and Image Cryptography 非自治不相称分数阶摆动系统的计算分析：混沌、控制和图像密码

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-10-02 DOI: 10.1155/cmm4/5351460

Sabrina Riah, Adel Ouannas, Giuseppe Grassi, Abdulmajeed Alsubhi, Noureddine Djenina, Imane Zouak

{"title":"Computational Analysis of a Nonautonomous Incommensurate Fractional-Order Swing System: Chaos, Control, and Image Cryptography","authors":"Sabrina Riah, Adel Ouannas, Giuseppe Grassi, Abdulmajeed Alsubhi, Noureddine Djenina, Imane Zouak","doi":"10.1155/cmm4/5351460","DOIUrl":"https://doi.org/10.1155/cmm4/5351460","url":null,"abstract":"In this paper, the dynamic behavior of an incommensurate fractional-order single-machine infinite-bus (IFOSMIB) power system is investigated through numerical simulations. Different dynamical phenomena are observed in the IFOSMIB system, including periodic oscillations, period-doubling bifurcations, and chaotic attractors. Furthermore, the complexity of the system dynamics is quantified using the complexity measure C0. In addition, the positivity of the largest Lyapunov exponent (LLE) and the results of the 0–1 test for chaos, a robust indicator for distinguishing regular dynamics from chaotic dynamics, confirm the existence of chaos in the system. Moreover, an effective control scheme is proposed to suppress the chaotic oscillations of the IFOSMIB power system, and its effectiveness is verified through numerical simulations. Furthermore, the proposed fractional-order chaotic system is investigated for information security applications. Its complex and highly sensitive dynamics are exploited in the development of a chaos-based encryption scheme, in which the generated chaotic sequences are employed for secure data encryption. The obtained results demonstrate the potential of the proposed system for cryptographic and secure communication applications.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/5351460","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Poisson-Gamma Trigonometric Families of Cure Fraction Models: Estimation and Analysis of Cancer Data 治愈分数模型的泊松-伽玛三角族：癌症数据的估计和分析

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-09-24 DOI: 10.1155/cmm4/4897525

Kingsley Kuwubasamni Ajongba, Suleman Nasiru, Jakperik Dioggban

{"title":"Poisson-Gamma Trigonometric Families of Cure Fraction Models: Estimation and Analysis of Cancer Data","authors":"Kingsley Kuwubasamni Ajongba, Suleman Nasiru, Jakperik Dioggban","doi":"10.1155/cmm4/4897525","DOIUrl":"https://doi.org/10.1155/cmm4/4897525","url":null,"abstract":"Sustainable Development Goal 3 has established clear targets to combat noncommunicable diseases (NCDs) such as cancer and cardiovascular diseases among others by the year 2030. A handy technique to study cancer progression is to analyze patient survival over time to obtain precise results to enable for the establishment of cancer control mechanisms. The use of cure rate models for analyzing survival data with cured elements is more desirable than the standard survival analysis models. This study formulated the Poisson-gamma trigonometric families of cure rate models under the competing risks setup based on the Poisson-gamma cure rate model and the trigonometric families of distributions. Four special models are obtained from the proposed families. Maximum likelihood estimation technique was utilized for estimating the parameters of the developed families. The cure rate families are parameterized in terms of the cure term and diverse link functions such as logit, cauchit, Aranda-Ordaz, and skewed logit are utilized to determine the effects of covariates. Monte Carlo simulation study was conducted to determine the behavior of the maximum likelihood estimator. The applications of the proposed models were finally established using myeloma and acute myeloid leukemia datasets. The study revealed that the proposed cure rate models provided better fit to the cancer datasets compared with the candidate models.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/4897525","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Poisson-Gamma Trigonometric Families of Cure Fraction Models: Estimation and Analysis of Cancer Data 治愈分数模型的泊松-伽玛三角族：癌症数据的估计和分析

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-09-24 DOI: 10.1155/cmm4/4897525

Kingsley Kuwubasamni Ajongba, Suleman Nasiru, Jakperik Dioggban

{"title":"Poisson-Gamma Trigonometric Families of Cure Fraction Models: Estimation and Analysis of Cancer Data","authors":"Kingsley Kuwubasamni Ajongba, Suleman Nasiru, Jakperik Dioggban","doi":"10.1155/cmm4/4897525","DOIUrl":"https://doi.org/10.1155/cmm4/4897525","url":null,"abstract":"Sustainable Development Goal 3 has established clear targets to combat noncommunicable diseases (NCDs) such as cancer and cardiovascular diseases among others by the year 2030. A handy technique to study cancer progression is to analyze patient survival over time to obtain precise results to enable for the establishment of cancer control mechanisms. The use of cure rate models for analyzing survival data with cured elements is more desirable than the standard survival analysis models. This study formulated the Poisson-gamma trigonometric families of cure rate models under the competing risks setup based on the Poisson-gamma cure rate model and the trigonometric families of distributions. Four special models are obtained from the proposed families. Maximum likelihood estimation technique was utilized for estimating the parameters of the developed families. The cure rate families are parameterized in terms of the cure term and diverse link functions such as logit, cauchit, Aranda-Ordaz, and skewed logit are utilized to determine the effects of covariates. Monte Carlo simulation study was conducted to determine the behavior of the maximum likelihood estimator. The applications of the proposed models were finally established using myeloma and acute myeloid leukemia datasets. The study revealed that the proposed cure rate models provided better fit to the cancer datasets compared with the candidate models.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/4897525","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Computational Multiresolution Nonlinear Autoregressive Framework Based on Wavelet Decomposition and Support Vector Regression 基于小波分解和支持向量回归的计算多分辨率非线性自回归框架

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-09-15 DOI: 10.1155/cmm4/3218150

Sarbast Saeed Ismael, Najlaa Saad Ibrahim, Taha Hussein Ali

{"title":"A Computational Multiresolution Nonlinear Autoregressive Framework Based on Wavelet Decomposition and Support Vector Regression","authors":"Sarbast Saeed Ismael, Najlaa Saad Ibrahim, Taha Hussein Ali","doi":"10.1155/cmm4/3218150","DOIUrl":"https://doi.org/10.1155/cmm4/3218150","url":null,"abstract":"This study introduces a computational multiresolution nonlinear autoregressive framework based on wavelet decomposition and support vector regression (SVR) for time series exhibiting heterogeneous temporal dynamics. Conventional nonlinear autoregressive models typically rely on single-scale lagged observations, which may be insufficient when the underlying process contains long-run movements, medium-term cycles, and short-term fluctuations simultaneously. To address this limitation, the proposed framework embeds discrete wavelet-based multiresolution representations of lagged observations directly into the autoregressive structure. The nonlinear relationship is estimated using ε-insensitive SVR with a Gaussian kernel, providing a flexible nonlinear learning mechanism. Model performance is assessed through an extensive Monte Carlo simulation design under several controlled data-generating environments, including multiscale dynamics, localized shocks, volatility clustering, and heavy-tailed disturbances. A rolling one-step-ahead forecasting scheme is employed for out-of-sample comparison with a conventional single-scale SVR benchmark. The simulation results indicate that incorporating multiresolution information improves forecasting accuracy across replications under the examined simulation settings. An empirical application to monthly copper price returns further illustrates the practical relevance of the proposed framework. Overall, the findings demonstrate the value of multiresolution representations in nonlinear autoregressive modeling of complex time series.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/3218150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Computational Multiresolution Nonlinear Autoregressive Framework Based on Wavelet Decomposition and Support Vector Regression 基于小波分解和支持向量回归的计算多分辨率非线性自回归框架

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-09-15 DOI: 10.1155/cmm4/3218150

Sarbast Saeed Ismael, Najlaa Saad Ibrahim, Taha Hussein Ali

{"title":"A Computational Multiresolution Nonlinear Autoregressive Framework Based on Wavelet Decomposition and Support Vector Regression","authors":"Sarbast Saeed Ismael, Najlaa Saad Ibrahim, Taha Hussein Ali","doi":"10.1155/cmm4/3218150","DOIUrl":"https://doi.org/10.1155/cmm4/3218150","url":null,"abstract":"This study introduces a computational multiresolution nonlinear autoregressive framework based on wavelet decomposition and support vector regression (SVR) for time series exhibiting heterogeneous temporal dynamics. Conventional nonlinear autoregressive models typically rely on single-scale lagged observations, which may be insufficient when the underlying process contains long-run movements, medium-term cycles, and short-term fluctuations simultaneously. To address this limitation, the proposed framework embeds discrete wavelet-based multiresolution representations of lagged observations directly into the autoregressive structure. The nonlinear relationship is estimated using ε-insensitive SVR with a Gaussian kernel, providing a flexible nonlinear learning mechanism. Model performance is assessed through an extensive Monte Carlo simulation design under several controlled data-generating environments, including multiscale dynamics, localized shocks, volatility clustering, and heavy-tailed disturbances. A rolling one-step-ahead forecasting scheme is employed for out-of-sample comparison with a conventional single-scale SVR benchmark. The simulation results indicate that incorporating multiresolution information improves forecasting accuracy across replications under the examined simulation settings. An empirical application to monthly copper price returns further illustrates the practical relevance of the proposed framework. Overall, the findings demonstrate the value of multiresolution representations in nonlinear autoregressive modeling of complex time series.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/3218150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling Spiral Chaos in Predator–Prey Dynamics Using Implicit Integration Factor Schemes 利用隐式积分因子方法建模捕食-食饵动力学中的螺旋混沌

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-08-31 DOI: 10.1155/cmm4/2730019

Kolade M. Owolabi, Sonal Jain, Edson Pindza, Eben Maré

{"title":"Modeling Spiral Chaos in Predator–Prey Dynamics Using Implicit Integration Factor Schemes","authors":"Kolade M. Owolabi, Sonal Jain, Edson Pindza, Eben Maré","doi":"10.1155/cmm4/2730019","DOIUrl":"https://doi.org/10.1155/cmm4/2730019","url":null,"abstract":"This paper presents efficient implicit integration factor (IIF) methods as robust alternatives to classical finite difference schemes for the numerical solution of nonlinear time-dependent reaction–diffusion equations in one and two spatial dimensions. The proposed framework combines computational efficiency with methodological simplicity while maintaining high accuracy for stiff nonlinear systems. A rigorous convergence and stability analysis is carried out, complemented by stability-region plots that provide insight into the qualitative behavior of the proposed schemes. As a biologically relevant application, the methods are employed to investigate a two-dimensional predator–prey reaction–diffusion model exhibiting diffusion-driven instability. Extensive numerical simulations accurately capture the emergence of Turing patterns, spot and stripe formations, rotating spiral waves, and spiral chaos, illustrating how species dispersal and nonlinear interactions generate complex spatiotemporal population distributions. These ecological patterns provide valuable insight into species coexistence, spatial self-organization, and long-term ecosystem dynamics. Detailed implementation guidelines, discretization strategies, and parameter selection procedures are provided to facilitate reproducibility and practical adoption. The numerical experiments confirm the theoretical convergence and stability properties of the proposed schemes while demonstrating their efficiency for large-scale ecological simulations. To encourage further research and reproducibility, open-access code implementing the second-order IIF scheme for predator–prey reaction–diffusion systems is also provided.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2730019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling Spiral Chaos in Predator–Prey Dynamics Using Implicit Integration Factor Schemes 利用隐式积分因子方法建模捕食-食饵动力学中的螺旋混沌

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-08-31 DOI: 10.1155/cmm4/2730019

Kolade M. Owolabi, Sonal Jain, Edson Pindza, Eben Maré

{"title":"Modeling Spiral Chaos in Predator–Prey Dynamics Using Implicit Integration Factor Schemes","authors":"Kolade M. Owolabi, Sonal Jain, Edson Pindza, Eben Maré","doi":"10.1155/cmm4/2730019","DOIUrl":"https://doi.org/10.1155/cmm4/2730019","url":null,"abstract":"This paper presents efficient implicit integration factor (IIF) methods as robust alternatives to classical finite difference schemes for the numerical solution of nonlinear time-dependent reaction–diffusion equations in one and two spatial dimensions. The proposed framework combines computational efficiency with methodological simplicity while maintaining high accuracy for stiff nonlinear systems. A rigorous convergence and stability analysis is carried out, complemented by stability-region plots that provide insight into the qualitative behavior of the proposed schemes. As a biologically relevant application, the methods are employed to investigate a two-dimensional predator–prey reaction–diffusion model exhibiting diffusion-driven instability. Extensive numerical simulations accurately capture the emergence of Turing patterns, spot and stripe formations, rotating spiral waves, and spiral chaos, illustrating how species dispersal and nonlinear interactions generate complex spatiotemporal population distributions. These ecological patterns provide valuable insight into species coexistence, spatial self-organization, and long-term ecosystem dynamics. Detailed implementation guidelines, discretization strategies, and parameter selection procedures are provided to facilitate reproducibility and practical adoption. The numerical experiments confirm the theoretical convergence and stability properties of the proposed schemes while demonstrating their efficiency for large-scale ecological simulations. To encourage further research and reproducibility, open-access code implementing the second-order IIF scheme for predator–prey reaction–diffusion systems is also provided.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2730019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Acceleration of Volume Integral Equations Using Trimmed Multilevel Fast Multipole Algorithm 基于修剪多层快速多极算法的体积积分方程加速

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-31 DOI: 10.1155/cmm4/6460608

Halil Topözlü, Barişcan Karaosmanoğlu, Vakur Behçet Ertürk

{"title":"Acceleration of Volume Integral Equations Using Trimmed Multilevel Fast Multipole Algorithm","authors":"Halil Topözlü, Barişcan Karaosmanoğlu, Vakur Behçet Ertürk","doi":"10.1155/cmm4/6460608","DOIUrl":"10.1155/cmm4/6460608","url":null,"abstract":"The concept of trimmed tree structures for multilevel fast multipole algorithm (MLFMA), referred to as trimmed-MLFMA (T-MLFMA), is proposed for the solution of volume integral equations for the fast analysis of scattering from large, inhomogeneous objects, where the conventional MLFMA suffers from high number of iterations and matrix vector multiplication (MVM) of large matrices at each iteration. In T-MLFMA, thresholding and machine learning techniques are used to eliminate the redundant interactions as the iterations proceed. In particular, the converged basis function coefficients are estimated with a fully connected neural network and, together with the thresholding, the MLFMA tree structure is systematically pruned, and the resulting far-interaction matrix becomes sparser. As a result, both the number of iterations and the MVM time per iteration are dramatically reduced. Using only a group of small homogeneous dielectric spheres with different permittivity values at the training stage, we are able to show that scattering from large, highly inhomogeneous and fairly complex objects are solved accurately and significantly faster than the conventional MLFMA solution (up to 10 times).","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/6460608","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148617331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures 非线性液体色散模式滴的分数动力学：调制不稳定性和紧致结构的鲁棒分析研究

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-28 DOI: 10.1155/cmm4/2166854

Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed

{"title":"Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures","authors":"Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed","doi":"10.1155/cmm4/2166854","DOIUrl":"https://doi.org/10.1155/cmm4/2166854","url":null,"abstract":"Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton-like structures, and clearly reveals the critical influence of the fractional-order parameter on modulation instability and nonlinear wave evolution. In this work, we present a systematic analytical investigation of nonlinear liquid dispersion drops governed by a time-fractional Rosenau–Hyman equation formulated in the notion of the Liouville–Caputo fractional derivative. The fractional framework allows the incorporation of memory effects that significantly influence the evolution of nonlinear dispersive waves. Using an efficient analytical scheme, approximate solutions are constructed and their dynamical behavior is examined for different fractional orders and physical parameters. The obtained results reveal the emergence of localized compacton-like structures that characterize nonlinear liquid dispersion patterns. To further understand the stability of these structures, a detailed modulation instability analysis is performed. The derived instability spectrum identifies the neutral stability boundaries and clarifies the conditions under which small perturbations grow and generate nonlinear wave structures. The systematic investigation demonstrates that the fractional order plays a crucial role in the formation of localized dispersion drops and controlling the instability growth rate. The present study provides new theoretical insights into nonlinear liquid dispersion mechanisms and offers a useful analytical framework for investigating complex wave dynamics in fractional dispersive media.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2166854","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0