Journal of Mathematical Chemistry最新文献_第3页

Numerical solution of fractal-fractional Lane–Emden equations using shifted legendre polynomials and operational matrices 利用移位勒让德多项式和运算矩阵的分形-分数阶Lane-Emden方程的数值解

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-08-20 DOI: 10.1007/s10910-026-01819-z

A. M. Shloof, Mohamed I. Nouh, Emad A. B. Abdel-Salam, Abaker A. Hassaballa

{"title":"Numerical solution of fractal-fractional Lane–Emden equations using shifted legendre polynomials and operational matrices","authors":"A. M. Shloof, Mohamed I. Nouh, Emad A. B. Abdel-Salam, Abaker A. Hassaballa","doi":"10.1007/s10910-026-01819-z","DOIUrl":"10.1007/s10910-026-01819-z","url":null,"abstract":"<div><p>This study presents a novel and efficient computational framework for numerically solving fractal-fractional Lane-Emden (FFLE) equations using the new generalized Caputo fractal-fractional derivative (NGCFFD). Lane-Emden equations arise naturally in modeling astrophysical phenomena such as stellar structure, polytropic gas spheres, and isothermal gas clouds, as well as in chemical kinetics, thermoelectric processes, and various branches of applied mathematics. The proposed technique employs shifted Legendre polynomials (SLPs) to construct an operational matrix that systematically transforms these complex fractal-fractional differential equations (FFDEs) into tractable systems of algebraic equations, applicable to both linear and nonlinear multi-order FFDEs. Six representative FFLE equations are investigated across twelve computational models with varying fractal-fractional parameters (<span>(upgamma )</span>, <span>(upbeta )</span>, <span>(uprho )</span>), and the results are rigorously compared against conformable fractional (CF) and modified Riemann–Liouville (mRL) solutions available in the literature. The proposed fractal-fractional models consistently outperform the corresponding standard Caputo models. An error estimation theorem and a convergence analysis confirm that the series solutions converge to the exact solutions in the Hilbert space <span>({L}^{2})</span>[0,1]. We think this is the first study to report a numerical solution of fractal-fractional Lane-Emden equations, establishing the fractal order parameter β as an essential, rather than merely supplementary, modeling component for certain classes of singular nonlinear problems.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 8","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strictly localized orbitals from spatial partitioning with the discontinuous Galerkin method 不连续伽辽金法空间划分的严格定域轨道

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-08-18 DOI: 10.1007/s10910-026-01823-3

César Feniou, Julien Toulouse

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A general informatic tool for treating solution equilibria in supramolecular chemistry 处理超分子化学中溶液平衡的通用信息工具

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-08-14 DOI: 10.1007/s10910-026-01818-0

Riccardo Salvio

{"title":"A general informatic tool for treating solution equilibria in supramolecular chemistry","authors":"Riccardo Salvio","doi":"10.1007/s10910-026-01818-0","DOIUrl":"10.1007/s10910-026-01818-0","url":null,"abstract":"<div><p>This work presents a versatile, open-source computational framework for the quantitative analysis of equilibria in solution, with particular emphasis on problems commonly encountered in supramolecular chemistry. The approach is based on a general numerical treatment of complex equilibrium systems, overcoming the limitations of analytical solutions that are restricted to only the simplest cases. The framework is implemented through a series of MATLAB scripts that are fully transparent, easily modifiable, and freely available, thereby avoiding the “black box” character of many commercial programs and enabling users to adapt the workflow to their specific experimental systems. The capabilities and performance of the tool are illustrated through its application to a range of representative datasets, including real experimental data acquired in the course of our own research activities. We demonstrate its utility for the analysis of host–guest complexation and acid–base titrations in which complexation phenomena are involved, thereby illustrating its reliability and broad applicability to recurring problems in supramolecular chemistry. At the same time, the methodology retains general validity for the treatment of almost any equilibrium process occurring in solution. By providing detailed documentation of the underlying mathematical and computational procedures, as well as complete access to the original scripts, this work promotes reproducibility and offers a flexible platform that can be readily employed to test mechanistic hypotheses and readily extended to address new and more elaborate systems.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01818-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","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 binomial approach to the stochastic kinetics of simple chemical reactions 简单化学反应随机动力学的二项式方法

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-08-12 DOI: 10.1007/s10910-026-01820-6

Gábor Lente

{"title":"A binomial approach to the stochastic kinetics of simple chemical reactions","authors":"Gábor Lente","doi":"10.1007/s10910-026-01820-6","DOIUrl":"10.1007/s10910-026-01820-6","url":null,"abstract":"<div><p>An approximate solution method is proposed to find the time dependence of the individual state probabilities in the master equation of the continuous time discrete state (CDS) stochastic kinetic approach. In systems where giving the number of a single type of molecule is enough to identify a state, this molecule number is assumed to show a binomial distribution whose expectation is the same as the solution of the corresponding deterministic rate equation. The approximation method is tested in ten different systems. In the first order reaction, it gives the exact solution of the stochastic master equation. In other systems, comparisons of expectations, standard deviations and distributions at selected reaction times with the exact ones at low initial molecule numbers show that the method gives reasonable results, whose precision is improved with an increase of initial molecule numbers. For the zeroth order process, a closed from for the exact solution of the master equation is also reported.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01820-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The unique equilibrium’s global exponential asymptotic stability of the irreversible Michaelis–Menten mechanism of enzyme kinetics 酶动力学的不可逆Michaelis-Menten机制的唯一平衡的全局指数渐近稳定性

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-27 DOI: 10.1007/s10910-026-01817-1

Benjamin Wacker

引用次数: 0

High-order multi-structures-preserving exponential integrators for the derivative nonlinear Schrödinger equation 导数非线性Schrödinger方程的高阶多结构保持指数积分器

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-25 DOI: 10.1007/s10910-026-01816-2

Liping Wu, Li Yang, Chaolong Jiang

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Optimal error estimates of the mass-preserving Galerkin finite element method for coupled nonlinear Schrödinger equations 耦合非线性Schrödinger方程保质量Galerkin有限元法的最优误差估计

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-20 DOI: 10.1007/s10910-026-01814-4

Lili Li, Wanqiu Yuan

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A higher-order Haar wavelet collocation method with Jacobian-free Newton solver for the Thomas–Fermi model equation Thomas-Fermi模型方程的高阶Haar小波配点法与无雅可比牛顿求解器

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-20 DOI: 10.1007/s10910-026-01815-3

Naaz Siddiqui, Sachin Sharma, Bharti Sharma

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Fractional-order chemostat model with Monod kinetics: analysis and efficient numerical approaches 莫诺动力学分数阶恒化模型：分析与有效数值方法

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-15 DOI: 10.1007/s10910-026-01813-5

Nagendra Kumar Yadav

{"title":"Fractional-order chemostat model with Monod kinetics: analysis and efficient numerical approaches","authors":"Nagendra Kumar Yadav","doi":"10.1007/s10910-026-01813-5","DOIUrl":"10.1007/s10910-026-01813-5","url":null,"abstract":"<div><p>This study proposes a multi-order fractional chemostat model with a Monod functional response to investigate the influence of memory effects on microbial growth dynamics. The classical integer-order formulation is generalized using Caputo fractional derivatives to capture the non-local hereditary characteristics frequently observed in biochemical systems. Fundamental qualitative properties, including the positivity and uniform boundedness of solutions, are rigorously established to ensure biological feasibility. Furthermore, a detailed local stability analysis is performed; the local asymptotic stability criteria for both the washout and coexistence equilibria are mathematically derived via Matignon’s criterion, establishing the parameter thresholds governing microbial extinction and persistence. To simulate the system, efficient numerical approximations are developed using the high-order Toufik–Atangana scheme and the fractional Adams–Bashforth–Moulton predictor–corrector method. Their computational performance is comparatively analyzed, demonstrating that the Toufik–Atangana scheme reduces mathematical complexity through efficient history-weighting loops. Numerical simulations reveal that fractional memory significantly modifies both transient and steady-state behaviors. Specifically, memory effects induce smoother state transitions and slower convergence toward equilibrium states compared to the classical integer-order system. These findings highlight the value of fractional-order modeling in capturing realistic microbial dynamics and provide an effective computational framework for evaluating non-linear bioreactor and ecological processes with memory.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 6","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analytical modeling of substrate inhibition kinetics in immobilized enzyme systems using the Hosoya polynomial approximation method 用细谷多项式近似法对固定化酶体系的底物抑制动力学进行分析建模

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-07-14 DOI: 10.1007/s10910-026-01807-3

M. Bhuvaneswari, V. Vinoba, R. Ganesh, G. Hariharan

{"title":"Analytical modeling of substrate inhibition kinetics in immobilized enzyme systems using the Hosoya polynomial approximation method","authors":"M. Bhuvaneswari, V. Vinoba, R. Ganesh, G. Hariharan","doi":"10.1007/s10910-026-01807-3","DOIUrl":"10.1007/s10910-026-01807-3","url":null,"abstract":"<div><p>This study presents an analytical investigation of substrate concentration profiles in immobilized enzyme systems exhibiting hysteresis behavior under enzyme flow calorimetry conditions. A mathematical model is formulated using the ordinary differential equations that incorporate nonlinear substrate inhibition kinetics together with diffusion parameters. Closed-form analytical expressions for the dimensionless substrate concentration at steady state are derived for planar, cylindrical, and spherical particle geometries using the Hosoya Polynomial Approximation Method (HPAM). The solution is expressed in terms of a quadratic polynomial basis constructed from path-graph Hosoya polynomials, whose coefficients are determined by satisfying the governing nonlinear boundary value problem at selected collocation points. The accuracy of HPAM is rigorously assessed by comparing its predictions against numerical solutions obtained via the fourth-order Runge–Kutta (RK4) method and against results from the Homotopy perturbation method (HPM). For all six parameter cases examined, HPAM achieves an average percentage deviation from the RK4 numerical solution as low as 0.0004% for planar particles (Table 1, β = 0.1) and below 1.69% even under the most demanding Thiele modulus conditions (Table 4, Ω = 260). In every case, HPAM outperforms HPM, which reaches deviations exceeding 10% under comparable conditions. A sensitivity analysis reveals that increasing the Thiele modulus Ω or decreasing the dimensionless inhibition parameter β amplifies the concentration gradient within the particle, a trend captured faithfully by the proposed method. The simplicity, accuracy, and broad applicability of HPAM makes it a valuable analytical tool for modeling reaction–diffusion systems in immobilized enzyme bioreactor design and kinetic parameter estimation.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 6","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0