Mathematical Methods in the Applied Sciences最新文献

{"title":"Existence, Uniqueness and Stability of Strictly Positive Entire Solutions to a Fractional Keller-Segel Model With Time-Space Dependent Logistic Source","authors":"Weiyi Zhang,&nbsp;Zuhan Liu,&nbsp;Ling Zhou","doi":"10.1002/mma.70586","DOIUrl":"https://doi.org/10.1002/mma.70586","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is devoted to the study of the asymptotic dynamics in the fractional parabolic-elliptic Keller-Segel system on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^N $$</annotation>\u0000 </semantics></math> with time-space dependent logistic source. In [36], among others, we established a theory on the global existence, uniqueness, pointwise and uniform persistence of classical solutions to this fractional Keller-Segel system. In this paper, we prove the existence, uniqueness, and stability of strictly positive entire solutions of this system. In summary, the results of our paper extend some of the results obtained earlier in [36].</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10204-10225"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343155","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":"A New Approach of Cryptographic Application via Unique Fixed Point Results in \u0000 \u0000 \u0000 \u0000 C\u0000 *\u0000 \u0000 \u0000 $$ {C}^{ast } $$\u0000 -Algebra Valued \u0000 \u0000 \u0000 b\u0000 \u0000 $$ b $$\u0000 -Metric Spaces","authors":"Saif Ur Rehman,&nbsp;Faiz Ullah,&nbsp;Muhammed Imran Haider,&nbsp;Sidra Akbar,&nbsp;Mehmet Emir Köksal","doi":"10.1002/mma.70604","DOIUrl":"https://doi.org/10.1002/mma.70604","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study unique fixed-point outcomes in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^{ast } $$</annotation>\u0000 </semantics></math>-algebra valued <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 <mo>-</mo>\u0000 </mrow>\u0000 <annotation>$$ bhbox{-} $$</annotation>\u0000 </semantics></math>metric space and their approach to constructing a chaotic system. We demonstrate some fixed-point theorems without requiring the continuity of self-mappings in the said space. In favor of our findings, we establish a nontrivial illustrative example to prove the uniqueness of fixed-point. In addition to validating our results, we present a line graph based on numerical examples to verify the inequality of our single-valued contraction condition in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <mo>-</mo>\u0000 <mtext>algebra valued</mtext>\u0000 <mspace></mspace>\u0000 <mi>b</mi>\u0000 <mo>-</mo>\u0000 <mtext>metric space</mtext>\u0000 </mrow>\u0000 <annotation>$$ {C}^{ast}hbox{-} mathrm{algebra} mathrm{valued} bhbox{-} mathrm{metric} mathrm{space} $$</annotation>\u0000 </semantics></math>. Moreover, we construct a computationally efficient chaotic system for a cryptographic algorithm using a unique fixed-point of a single-valued contraction condition. However, a fixed-point contraction itself can hardly fulfill chaotic phenomena. In this connection, we design a jumping algorithm for generating large-scale chaotic data output around fixed-point. Meanwhile, we validate the chaos feature of the proposed algorithm via Lyapunov and bifurcation representation.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10366-10377"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343204","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":"Asymptotic Flocking Dynamics of Relativistic–Cucker–Smale Particles Immersed in Incompressible Navier–Stokes Equations","authors":"Shenglun Yan,&nbsp;Weiyuan Zou","doi":"10.1002/mma.70581","DOIUrl":"https://doi.org/10.1002/mma.70581","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we propose a coupled system that describes the interaction between the Relativistic–Cucker–Smale (RCS) model and the incompressible Navier–Stokes equations through a drag force on the 3D torus <span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>𝕋</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math>. The model captures the collective dynamics of high-speed particles immersed in a low-speed background fluid. We first establish the global existence of weak solutions for large initial data. Furthermore, under suitable assumptions, we prove that the coupled system exhibits exponential asymptotic alignment between the RCS particles and the surrounding fluid. The main analytical challenge arises from handling the strong nonlinearity induced by the relativistic velocity mapping.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10033-10066"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343154","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":"New Results on Quasi-Dynamic Analysis of Quaternion-Valued Memristive Neural Networks on Time Scales","authors":"Ruoxia Li,&nbsp;Yuxing Zhu,&nbsp;Xuguang Wei,&nbsp;Jinde Cao,&nbsp;Zhao-Dong Xu","doi":"10.1002/mma.70582","DOIUrl":"https://doi.org/10.1002/mma.70582","url":null,"abstract":"<div>\u0000 \u0000 <p>This note solves the quasi-stability/synchronization for memristive neural networks on time scales. A novel Lemma is given to estimate the modulus of the quaternions, which avoids comparing the “size” of quaternions. Subsequently, a new scale-limited Halanay inequality is given to solve the quasi-synchronization control of the system in the time-scale domain. The validity of the theoretical results is illustrated by two examples.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10226-10238"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343159","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":"POD Method for the Inverse Initial Value Problem of Two-Dimensional Time-Fractional Diffusion Equation and Application to Image Deblurring","authors":"Jin Wen,&nbsp;Hong-Bo Zheng","doi":"10.1002/mma.70591","DOIUrl":"https://doi.org/10.1002/mma.70591","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we mainly investigate the backward problem for the two-dimensional time-fractional diffusion equation by the proper orthogonal decomposition (POD) method, and also apply this method to solve the image deblurring problem. The approach constructs a low-dimensional basis by solution snapshots to accelerate the reconstruction of the initial field from noisy terminal time measurements. Besides, we give the Tikhonov regularization method and obtain the convergence analysis about the regularization solutions. Finally, we propose several numerical experiments to show the efficiency and accuracy of our method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10173-10189"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148342991","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":"Stochastic SIQS Epidemic Model With General Incidence Rate","authors":"B. Harchaoui,&nbsp;M. Esseroukh,&nbsp;B. El Khatib,&nbsp;A. Settati,&nbsp;A. Lahrouz,&nbsp;I. Bouzalmat","doi":"10.1002/mma.70593","DOIUrl":"https://doi.org/10.1002/mma.70593","url":null,"abstract":"<div>\u0000 \u0000 <p>This research comprehensively examines a stochastic SIQS epidemic model, incorporating a general incidence rate <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 <mi>I</mi>\u0000 </mrow>\u0000 <annotation>$$ beta g(S)I $$</annotation>\u0000 </semantics></math>. In order to better understand the intricate dynamics of the disease, we investigate using a stochastic model for the COVID-19 epidemic, which includes a compartment designed to represent quarantined populations. Specifically, we demonstrate that a generalized stochastic threshold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℛ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_s(g) $$</annotation>\u0000 </semantics></math> determines the conditions under which the disease either goes extinct or persists. We delve into the critical scenario when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℛ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_s(g)=1 $$</annotation>\u0000 </semantics></math>. Finally, we illustrate our analytical findings through a comprehensive series of computer simulations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10190-10203"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343111","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":"Blow-Up in the Critical Quasilinear Keller–Segel System With Indirect Signal Production","authors":"Taian Jin,&nbsp;Yuxiang Li","doi":"10.1002/mma.70588","DOIUrl":"https://doi.org/10.1002/mma.70588","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We study the Neumann initial-boundary value problem for the following quasilinear chemotaxis system with indirect signal production &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;/mtr&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10149-10172"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343110","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":"Energy Transfer and Interaction Mechanism of Kink-Antikink Waves in Nonlinear Media","authors":"U. Akram,&nbsp;N. A. Alreshidi","doi":"10.1002/mma.70580","DOIUrl":"https://doi.org/10.1002/mma.70580","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Nonlinear wave equations have attracted broad interest due to their numerous applications in physics, engineering, and applied mathematics. Kink-antikink interactions are a key phenomenon in nonlinear dynamics, providing insights into energy transfer, soliton collisions, and wave propagation in dispersive and nonlinear media. This study examines kink-antikink interactions in the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}^4 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;6&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {v}^6 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; models utilizing collective coordinates and computational methods. Here, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}^4 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;6&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {v}^6 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; represent models of scalar fields which are influenced by fourth- and sixth-order nonlinear potentials, respectively. The &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}^4 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; model has two degenerate vacuum states, while the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;6&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/ms","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10067-10107"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343253","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":"Optimal Stabilizing Random Output Feedback for Boolean Networks With Random Data Loss","authors":"Hongliang Zhang,&nbsp;Yuqian Guo,&nbsp;Weihua Gui","doi":"10.1002/mma.70579","DOIUrl":"https://doi.org/10.1002/mma.70579","url":null,"abstract":"<div>\u0000 \u0000 <p>This study addresses the issue of asymptotic stabilization of Boolean control networks (BCNs) through output feedback in the presence of random data loss in both output measurements and control signals. We utilize a random output feedback (ROF) strategy that employs interpolation models to compensate for missing data. A poset-based criterion is established to determine the asymptotic stabilizability of BCNs under ROFs. Importantly, we demonstrate that data loss does not undermine asymptotic stabilizability, provided that the probability of data loss is strictly less than one. Furthermore, we explore the problem of designing an optimal stabilizing ROF. An algorithm is presented to compute the optimal stabilizing ROF based on linear matrix inequalities (LMIs) with equality constraints. The proposed method is applied to control a simplified BCN model for the lac operon in the bacterium <i>Escherichia coli</i>. The results reveal that the optimal ROF strategy outperforms the optimal deterministic output feedback (DOF) strategy.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10133-10148"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343255","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":"Closed-Form Exact Solitary-Wave Solutions for the Time-Fractional Rosenau-KdV-RLW Equation","authors":"Nauman Ahmed,&nbsp;Jorge E. Macías-Díaz,&nbsp;Shazia Umer,&nbsp;Muhammad Zafarullah Baber,&nbsp;Ali Raza,&nbsp;María Guadalupe Medina-Guevara","doi":"10.1002/mma.70598","DOIUrl":"https://doi.org/10.1002/mma.70598","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we investigate exact solitary-wave solutions of the time-conformable Rosenau Korteweg de Vries (R-KdV) regularized long-wave equation, extended through a power-law nonlinearity. A specific form of the modified R-KdV equation is addressed, and closed-form solitary-wave solutions are derived using the well-established generalized Riccati equation mapping (GREM) technique. Initially, the conformable time-fractional R-KdV equation is transformed into a nonlinear ordinary differential equation (ODE) through a nonlinear conformable time transformation. The GREM method is then applied to obtain exact analytical solutions of the resulting model. This approach yields various classes of solutions, including both solitons and solitary waves. The derived solutions include singular waves, bright and dark solitons, as well as other localized wave structures. To support the physical interpretation of the results, we present two-dimensional (2D), three-dimensional (3D), and contour plots for different parameter settings. These graphical representations illustrate the qualitative behavior of the waveforms and highlight the impact of model parameters on the soliton dynamics.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10417-10429"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343301","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}