数学最新文献

{"title":"Existence and uniqueness of time-periodic solutions to the Oberbeck–Boussinesq system","authors":"Tomoyuki Nakatsuka","doi":"10.1016/j.nonrwa.2025.104461","DOIUrl":"10.1016/j.nonrwa.2025.104461","url":null,"abstract":"<div><div>This paper is devoted to the study of the time-periodic problem for the Oberbeck–Boussinesq system in the whole space. Our investigation is based on the reformulation of the time-periodic problem and does not depend on the analysis of the initial value problem. We construct a time-periodic solution with more information on its structure than the solutions in preceding studies. We also prove that our solution, small in an appropriate sense, is unique in the class of solutions having slightly more regularity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104461"},"PeriodicalIF":1.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Continuum limit of fourth-order Schrödinger equations on the lattice","authors":"Jiawei Cheng,&nbsp;Bobo Hua","doi":"10.1112/jlms.70247","DOIUrl":"https://doi.org/10.1112/jlms.70247","url":null,"abstract":"<p>In this paper, we consider the discrete fourth-order Schrödinger equation on the lattice <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$hmathbb {Z}^2$</annotation>\u0000 </semantics></math>. Uniform Strichartz estimates are established by analyzing frequency localized oscillatory integrals with the method of stationary phase and applying Littlewood–Paley inequalities. As an application, we obtain the precise rate of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math> convergence from the solutions of discrete semilinear equations to those of the corresponding equations on the Euclidean plane <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> in the continuum limit <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>→</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$h rightarrow 0$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144716597","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":"Q-points, selective ultrafilters, and idempotents, with an application to choiceless set theory","authors":"David Fernández-Bretón,&nbsp;Jareb Navarro-Castillo,&nbsp;Jesús A. Soria-Rojas","doi":"10.1112/jlms.70249","DOIUrl":"https://doi.org/10.1112/jlms.70249","url":null,"abstract":"&lt;p&gt;We study ultrafilters from the perspective of the algebra in the Čech–Stone compactification of the natural numbers, and idempotent elements therein. The first two results that we prove establish that, if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a Q-point (resp., a selective ultrafilter) and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathcal F^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (resp., &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathcal G^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) is the smallest family containing &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and closed under iterated sums (resp., closed under Blass–Frolík sums and Rudin–Keisler images), then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathcal F^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (resp., &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathcal G^p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) contains no idempotent elements. The second of these results about a selective ultrafilter has the following interesting consequence: assuming a conjecture of Blass, in models of the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathnormal {mathbf {L}(mathbb {R})}[p]$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathnormal {mathbf {L}(mathbb {R})}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a Solovay model (of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ZF&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathnormal {mathsf {ZF}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; without choice) and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a selective ultrafilter, there are no idempotent elements. In particular, the theory &lt;sp","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144716702","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":"Perfect k-matching, k-factor-critical and Aα-spectral radius","authors":"Mengyuan Niu ,&nbsp;Shanshan Zhang ,&nbsp;Xiumei Wang","doi":"10.1016/j.dam.2025.07.020","DOIUrl":"10.1016/j.dam.2025.07.020","url":null,"abstract":"<div><div>A <span><math><mi>k</mi></math></span>-<em>matching</em> of a graph <span><math><mi>G</mi></math></span> is a function <span><math><mi>f</mi></math></span>: <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>→</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></mrow></math></span> satisfying <span><math><mrow><munder><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><mi>∂</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></munder><mi>f</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mo>≤</mo><mi>k</mi></mrow></math></span> for any vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. A <span><math><mi>k</mi></math></span>-matching of a graph <span><math><mi>G</mi></math></span> is <em>perfect</em> if <span><math><mrow><munder><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><mi>∂</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></munder><mi>f</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mo>=</mo><mi>k</mi></mrow></math></span> for every vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. A graph <span><math><mi>G</mi></math></span> of order <span><math><mi>n</mi></math></span> is <em>k-factor-critical</em> if the removal of any set of <span><math><mi>k</mi></math></span> vertices of <span><math><mi>G</mi></math></span> results in a graph with a perfect matching. Let <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> be the adjacency matrix and the degree diagonal matrix of <span><math><mi>G</mi></math></span>. For <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, Nikiforov <span><math><mrow><mo>(</mo><mn>2017</mn><mo>)</mo></mrow></math></span> introduced the <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-matrix of G as follows: <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><mi>D</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow><mi>A</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span> In this paper, according to the <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-spectral radius, we provide two sufficient conditions to ensure that a graph is <span><math><mi>k</mi></math></span>-factor-critical and has a perfect <span><math><mi>k</mi></math></span>-matching, respectively.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"376 ","pages":"Pages 384-393"},"PeriodicalIF":1.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Indivisibility for classes of graphs","authors":"Vincent Guingona ,&nbsp;Felix Nusbaum ,&nbsp;Zain Padamsee ,&nbsp;Miriam Parnes ,&nbsp;Christian Pippin ,&nbsp;Ava Zinman","doi":"10.1016/j.disc.2025.114703","DOIUrl":"10.1016/j.disc.2025.114703","url":null,"abstract":"<div><div>We examine indivisibility for classes of graphs. We show that the class of hereditarily <em>α</em>-sparse graphs is indivisible if and only if <span><math><mi>α</mi><mo>&gt;</mo><mn>2</mn></math></span>. Additionally, we show that the following classes of graphs are indivisible: perfect graphs, cographs, and chordal graphs, and the following classes of graphs are not indivisible: threshold graphs, split graphs, and distance-hereditary graphs.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114703"},"PeriodicalIF":0.7,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the complexity of p-order cone programs","authors":"Víctor Blanco ,&nbsp;Victor Magron ,&nbsp;Miguel Martínez-Antón","doi":"10.1016/j.jco.2025.101979","DOIUrl":"10.1016/j.jco.2025.101979","url":null,"abstract":"<div><div>This manuscript explores novel complexity results for the feasibility problem over <em>p</em>-order cones, extending the foundational work of Porkolab and Khachiyan (1997) <span><span>[30]</span></span>. By leveraging the intrinsic structure of <em>p</em>-order cones, we derive refined complexity bounds that surpass those obtained via standard semidefinite programming reformulations. Our analysis not only improves theoretical bounds but also provides practical insights into the computational efficiency of solving such problems. In addition to establishing complexity results, we derive explicit bounds for solutions when the feasibility problem admits one. For infeasible instances, we analyze their discrepancy quantifying the degree of infeasibility. Finally, we examine specific cases of interest, highlighting scenarios where the geometry of <em>p</em>-order cones or problem structure yields further computational simplifications. These findings contribute to both the theoretical understanding and practical tractability of optimization problems involving <em>p</em>-order cones.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"91 ","pages":"Article 101979"},"PeriodicalIF":1.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724397","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":"Reverse order law for NDMPI of dual complex matrices and its applications","authors":"Tikesh Verma, Amit Kumar, Debasisha Mishra","doi":"10.1080/03081087.2025.2537965","DOIUrl":"https://doi.org/10.1080/03081087.2025.2537965","url":null,"abstract":"","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144737009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A topological algorithm for the Fourier transform of Stokes data at infinity","authors":"Jean Douçot,&nbsp;Andreas Hohl","doi":"10.1112/jlms.70253","DOIUrl":"https://doi.org/10.1112/jlms.70253","url":null,"abstract":"<p>We give a topological description of the behaviour of Stokes matrices under the Fourier transform from infinity to infinity in a large number of cases of one level. This explicit, algorithmic statement is obtained by building on a recent result of T. Mochizuki about the Fourier transform of Stokes data of irregular connections on the Riemann sphere and by using the language of Stokes local systems due to P. Boalch. In particular, this induces explicit isomorphisms between wild character varieties, in a much larger range of examples than those for which such isomorphisms have previously been written down. We conjecture that these isomorphisms are compatible with the quasi-Hamiltonian structure on the wild character varieties.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70253","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144716703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Synergistic effects of feedback regulation and vegetation internal competition on vegetation patterns in semi-arid environments","authors":"Feiran Li,&nbsp;Ruizhi Yang,&nbsp;Liqin Liu","doi":"10.1016/j.chaos.2025.116912","DOIUrl":"10.1016/j.chaos.2025.116912","url":null,"abstract":"<div><div>Against the backdrop of global aridification, the spatial self-organization of vegetation in semi-arid regions is critical to ecosystem stability. This study employs mathematical modeling to unravel the synergistic effects of soil–water diffusion feedback (<span><math><mi>β</mi></math></span>) and vegetation internal competition (<span><math><mi>σ</mi></math></span>) on pattern formation. Extending the Klausmeier framework, we integrate a cross-diffusion term <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><mi>w</mi><mo>−</mo><mi>β</mi><mi>n</mi><mo>)</mo></mrow></mrow></math></span> for root-driven soil–water feedback and a density-dependent competition term <span><math><mrow><mn>1</mn><mo>+</mo><mi>σ</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. Key findings include: (1) Increasing <span><math><mi>β</mi></math></span> drives sequential transitions from homogeneous states to gap, stripe, and spot patterns, while rising <span><math><mi>σ</mi></math></span> induces reverse transitions, revealing their antagonistic roles in stability; (2) Enhanced precipitation promotes the expansion of discrete spots into continuous stripes, eventually forming gaps under water surplus. Root-mediated water uptake balances short-term facilitation and long-term competition, explaining adaptive responses to resource constraints. Spot patterns act as desertification warnings, whereas stripes offer restoration strategies via high water-use efficiency. By merging cross-diffusion and competition mechanisms, this work proposes a theoretical framework for arid land management, linking mechanistic insights to practical solutions against land degradation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116912"},"PeriodicalIF":5.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid computational and ANN-based analysis of heat transfer and bioconvection in Sutterby nanofluid flow across a stretched surface","authors":"M. Waqas Ashraf ,&nbsp;M. Israr Ur Rehman ,&nbsp;Zhoushun Zheng ,&nbsp;Aamir Hamid ,&nbsp;Haitao Qi","doi":"10.1016/j.chaos.2025.116942","DOIUrl":"10.1016/j.chaos.2025.116942","url":null,"abstract":"<div><div>This study presents the application of computational fluid dynamics in conjunction with artificial neural networks to analyze the heat and mass transfer characteristics of bioconvective Sutterby nanofluid over a two-dimensional stretching sheet. The Darcy-Forchheimer model evaluates porous media resistance in the presence of chemical reactions. By applying suitable similarity transformations, the governing equations are transformed into a non-dimensional form and solved numerically using the bvp4c approach. Additionally, an ANN model is developed and trained using the Levenberg–Marquardt Backpropagation algorithm (LMBP) to accurately predict skin friction, Nusselt number, Sherwood number, and the concentration of motile microorganisms. It can be concluded that the Darcy and Deborah numbers exhibit a similar increasing trend within the velocity profile. The Brownian motion parameter has the opposite effect on thermal distribution and the mass transport rate. The ANN predictions and numerical results for heat and mass transfer showed excellent agreement. The optimized ANN model accurately predicted critical parameters with a variance of <span><math><mo>±</mo><mn>2</mn><mo>%</mo></math></span> and a maximum error of <span><math><mn>1.8</mn><mo>%</mo></math></span> in all scenarios. This demonstrates the efficacy of the hybrid computational and ANN framework in simulating the complex flow and heat transfer properties of nanofluids on stretched surfaces.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116942"},"PeriodicalIF":5.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}