Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Fractional differential equations with continuous variable coefficients and Sonine kernels","authors":"Yıldız Güzoğlu Yücel ,&nbsp;Arran Fernandez ,&nbsp;Nazim I. Mahmudov","doi":"10.1016/j.cnsns.2025.109136","DOIUrl":"10.1016/j.cnsns.2025.109136","url":null,"abstract":"<div><div>We study linear fractional ODEs with continuous variable coefficients and general fractional derivative (GFD) operators of Riemann–Liouville and Caputo types defined using Sonine kernels. Using the Banach fixed point theorem, we prove existence and uniqueness of solution functions in suitable function spaces, and we construct these solutions explicitly by means of locally uniformly convergent infinite series involving Sonine kernels. This work is done both for the classical Luchko-type GFDs with Sonine kernels, and for the <span><math><mi>m</mi></math></span>-fold versions of these operators.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109136"},"PeriodicalIF":3.4,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lattice Boltzmann method with a PML technique for pricing American lookback put options","authors":"Fangfang Wu,&nbsp;Shuangyi Wang,&nbsp;Xiaoxiao Dong,&nbsp;Ming Tian","doi":"10.1016/j.cnsns.2025.109149","DOIUrl":"10.1016/j.cnsns.2025.109149","url":null,"abstract":"<div><div>This paper proposes an efficient lattice Boltzmann method (LBM) with the perfectly matched layer (PML) technique for pricing American lookback put options. The pricing model for American lookback put options is formulated as a two-dimensional linear complementarity problem (LCP) on an unbounded domain. First, by using variable substitution and the penalty method, the LCP is transformed into a one-dimensional unbounded parabolic problem. To address the unbounded domain, a PML technique is introduced to truncate it. Subsequently, an effective lattice Boltzmann model is developed to solve the resulting bounded nonlinear parabolic problem. By selecting the appropriate equilibrium distribution functions and amending functions, the macroscopic equation is recovered. Finally, several numerical simulations are conducted to validate the efficiency of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109149"},"PeriodicalIF":3.4,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The principal chiral field equation: Novel exact solutions and soliton surface analysis","authors":"Xue-Ke Liu ,&nbsp;Zhen Wang ,&nbsp;Xiao-Yong Wen","doi":"10.1016/j.cnsns.2025.109143","DOIUrl":"10.1016/j.cnsns.2025.109143","url":null,"abstract":"<div><div>This paper investigates the principal chiral field equation possessing asymptotic freedom and dimensional transmutation. Firstly, we prove that the principal chiral field equation is gauge equivalent to a reduced Hirota-Maxwell–Bloch equation, potentially describing the propagation of self-induced transparency solitons in erbium doped fiber. Then the <span><math><mi>N</mi></math></span>-fold Darboux transformation is used to generate some novel multiple soliton and breather structures such as ‘Z’-shaped, ‘V’-shaped and snakelike structures, which differ from conventional solitons and breathers. Through the asymptotic analysis, we graphically depict the propagation trajectories of two-soliton and reveal the elastic collision characteristic of solitons. Furthermore, we observe that there may exist the energy transfer among these components of the principal chiral field equation when the seed solution is constant. Finally, we analyze the soliton surfaces by the Sym formula to elucidate the connection between the principal chiral field equation and geometry. Our findings may contribute valuable insights to the investigation of chiral fields.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109143"},"PeriodicalIF":3.4,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence, global attractiveness and stability of higher-order fractional stochastic hemivariational inequalities with non-instantaneous impulses","authors":"Zuomao Yan,&nbsp;Tainian Zhang","doi":"10.1016/j.cnsns.2025.109137","DOIUrl":"10.1016/j.cnsns.2025.109137","url":null,"abstract":"<div><div>In this article, a new class higher-order fractional stochastic hemivariational inequalities with non-instantaneous impulses and infinite delay is considered. First, a suitable concept of solution to this system is formulated, and the existence of mild solutions on the half-line are demonstrated by using stochastic analysis, the measure of noncompactness, properties of <span><math><mi>α</mi></math></span>-order fractional resolvent operators and fixed point theorems. Second, we establish the global attracting set and weakly exponential stability of mild solutions to fractional stochastic hemivariational inequalities under the non-Lipschitz conditions. In the end, examples are given for the illustration of the obtained theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109137"},"PeriodicalIF":3.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved sampled-data synchronization in chaotic Lur’e systems via a two-layer LPV framework","authors":"Kaveh Hooshmandi ,&nbsp;Saleh Mobayen ,&nbsp;Abouzar Samimi","doi":"10.1016/j.cnsns.2025.109125","DOIUrl":"10.1016/j.cnsns.2025.109125","url":null,"abstract":"<div><div>This paper investigates the sampled-data exponential synchronization of chaotic Lur’e systems (CLSs) while meeting predefined <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> disturbance attenuation requirements. A novel two-layer polytopic linear parameter-varying (LPV) framework is proposed, which models the system based on sampled outputs and utilizes slope bounds to linearize the nonlinear error dynamics. By employing a piecewise differentiable Lyapunov–Krasovskii functional (LKF) and Wirtinger’s inequality, new sufficient conditions for global exponential synchronization are derived and expressed as linear matrix inequalities (LMIs). To enhance stability over extended sampling intervals, slack variable matrices are used to develop improved criteria for designing sampled-data <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> parameter-varying controllers. The integration of multiple controllers within a closed-loop system ensures superior stability compared to existing approaches. Numerical examples validate the effectiveness and advantages of the proposed method, demonstrating significant improvements over state-of-the-art techniques.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109125"},"PeriodicalIF":3.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traveling waves for a nonlocal dispersal multi-stable system in almost periodic structures","authors":"Lu Yang,&nbsp;Yongkun Li","doi":"10.1016/j.cnsns.2025.109117","DOIUrl":"10.1016/j.cnsns.2025.109117","url":null,"abstract":"<div><div>This study focuses on investigating traveling waves within a nonlocal dispersal multi-stable system characterized by almost periodic structures. The primary distinctions from earlier research lie in the diffusion components and the classification of the reaction terms. Findings regarding the stability and existence of almost automorphic (or periodic) traveling waves in scalar equations with Laplace diffusion are extended to nonlocal diffusion systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109117"},"PeriodicalIF":3.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact separable solutions of two-dimensional time-fractional nonlinear biological population model under the regularized Prabhakar and ψ-Hilfer fractional-order derivatives","authors":"P. Prakash ,&nbsp;Stéphane Victor ,&nbsp;Pavithra Raj","doi":"10.1016/j.cnsns.2025.109145","DOIUrl":"10.1016/j.cnsns.2025.109145","url":null,"abstract":"<div><div>The main aim of this work is to investigate how to compute the exact separable solutions using the invariant subspace method for the fractional-order time derivative of two-dimensional nonlinear partial differential equations involving two space and one-time variables under two different fractional-order derivative definitions, namely the regularized Prabhakar and <span><math><mi>ψ</mi></math></span>-Hilfer fractional-order derivatives. We also explicitly demonstrate the importance and usefulness of the method of the invariant subspace approach in computing the exact separable solutions for the two-dimensional fractional-order time derivative of the biological population model, which helps more accurately predict how populations will grow or shrink. More specifically, we show systematically how to compute the linear spaces for the above-mentioned model with the help of the invariant subspace approach. Furthermore, the computations of exact separable solutions are investigated for the linear and nonlinear biological population models under the above-mentioned two different time fractional-order derivatives with the help of the computed invariant linear spaces. Additionally, we notice that the computed solutions of the considered equations under the <span><math><mi>ψ</mi></math></span>-Hilfer fractional derivative are valid under the <span><math><mi>ψ</mi></math></span>-Riemann–Liouville, <span><math><mi>ψ</mi></math></span>-Caputo, Hilfer, Katugampola, Caputo–Katugampola, Riemann–Liouville, and Caputo fractional derivatives because the <span><math><mi>ψ</mi></math></span>-Hilfer fractional derivative is a generalization of those fractional derivatives. Also, note that the computed exact separable solutions to the underlying equation under two fractional-order derivatives are expressed in terms of trigonometric, exponential, and polynomial functions with two or three parameters of Mittag-Leffler functions. In addition, the obtained solutions under different fractional-order derivatives are compared with two-dimensional (2D) graphical representations. Finally, the exact separable solutions are presented for the initial and boundary value problems (IBVPs) of the discussed model under various fractional-order derivatives and their comparison.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109145"},"PeriodicalIF":3.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive fuzzy predefined-time control for uncertain nonlinear systems with hysteresis and time-varying constraints","authors":"Rui Meng ,&nbsp;Zhumu Fu ,&nbsp;Nan Wang ,&nbsp;Zhikai Wang ,&nbsp;Fazhan Tao","doi":"10.1016/j.cnsns.2025.109146","DOIUrl":"10.1016/j.cnsns.2025.109146","url":null,"abstract":"<div><div>This paper explores the adaptive fuzzy predefined-time and accuracy control problem for uncertain nonlinear systems with hysteresis input and asymmetric time-varying output constrains. Different from existing predefined-time control schemes that solely assign transient performance, a fractional-order feedback control framework with polymorphism characteristics is established to preset both convergence time and steady-state accuracy simultaneously. Firstly, an asymmetric barrier Lyapunov function is designed to prevent the output from violating asymmetric time-varying constraints. Secondly, a low-complexity adaptive approximation method is developed by estimating an intermediate auxiliary variable, which effectively compensates for the hysteresis nonlinearity. Then, by analyzing the relationship between the tracking error and the predefined accuracy, an observer-based predefined-time controller is constructed by utilizing adaptive control method and the dynamic surface control algorithm, which ensures that the tracking error converges to predefined accuracy range within predefined-time. Finally, the viability of the presented control strategy is verified by two simulation examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109146"},"PeriodicalIF":3.4,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simultaneous identification of fractional order and time-dependent source term of a time-fractional Black–Scholes equation","authors":"Hanghang Wu ,&nbsp;Hongqi Yang","doi":"10.1016/j.cnsns.2025.109133","DOIUrl":"10.1016/j.cnsns.2025.109133","url":null,"abstract":"<div><div>This paper investigates the simultaneous identification of both the fractional order and time-dependent source term in a time-fractional Black–Scholes equation. We first establish the uniqueness of solutions for this coupled nonlinear inverse problem. To address the inherent ill-posedness, we reformulate the inverse problem within a Bayesian inference framework, and an iterative regularized ensemble Kalman method is subsequently developed to solve the resulting statistical inverse problem. Finally, numerical examples show that the proposed method is effective and stable. Notably, we identify limitations of the iterative regularized ensemble Kalman method: its robustness diminishes when observational data contain high noise levels. Despite this, the method provides a foundational framework for future research on high-noise inverse problems in fractional systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109133"},"PeriodicalIF":3.4,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of a stochastic SAIVR epidemic model with vaccination","authors":"Feng Rao,&nbsp;Xin Li,&nbsp;Dandan Xue","doi":"10.1016/j.cnsns.2025.109113","DOIUrl":"10.1016/j.cnsns.2025.109113","url":null,"abstract":"<div><div>This paper introduces and investigates the dynamics of a stochastic <span><math><mrow><mi>S</mi><mi>A</mi><mi>I</mi><mi>V</mi><mi>R</mi></mrow></math></span> (Susceptible–Asymptomatic–Infected–Vaccinated–Recovered) epidemic model incorporating vaccination and environmental noise. The effects of these components are examined through both rigorous analysis and numerical simulations. We provide preliminary results, including the calculation of the basic reproduction number <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> for the deterministic model, along with the identification of equilibrium points. Based on the proof of existence and uniqueness of the global positive solution to the stochastic model, we first obtain the boundedness of the solution. Then, two critical thresholds, <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>s</mi></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup></math></span>, are established to characterize the conditions for disease persistence and extinction. The theoretical results of the stochastic model include sufficient conditions for the existence of a unique ergodic stationary distribution through the construction of appropriate stochastic Lyapunov functions; the explicit probability density function of the distribution by solving the Fokker–Planck equation; and long-term disease extinction conditions. Furthermore, numerical simulations are conducted to validate the theoretical results, and sensitivity analysis is performed to assess the impact of each parameter on disease transmission. Our findings reveal that the proposed model, incorporating vaccination and environmental noise, displays complex dynamics. Small environmental noise and vaccination rates may hinder disease extinction, while larger values can facilitate it, providing valuable insights for disease control in complex communities.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109113"},"PeriodicalIF":3.4,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}