Mathematical Methods in the Applied Sciences最新文献

{"title":"Rational function solutions of higher-order dispersive cubic-quintic nonlinear Schrödinger dynamical model and its applications in fiber optics","authors":"Muhammad Arshad,&nbsp;Faisal Yasin,&nbsp;Saud Fahad Aldosary,&nbsp;Hadi Rezazadeh,&nbsp;Muhammad Farman,&nbsp;Mohammad Ali Hosseinzadeh","doi":"10.1002/mma.10604","DOIUrl":"https://doi.org/10.1002/mma.10604","url":null,"abstract":"<p>The study explores a series of cubic-quintic nonlinear Schrödinger equation with higher-order dispersive characteristics. This equation is also a fundamental equation in nonlinear physics that is used to depict the dynamics of femtosecond light pulses propagating through a medium with a nonlinearity profile characterized by a parabolic function. Symbolic computation is utilized, and the double \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>′</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left({G}&amp;amp;amp;#x0005E;{prime }/G,1/Gright) $$</annotation>\u0000 </semantics></math>-expansion technique is applied to investigate the mathematical characteristics of this equation. Novel solitons and rational function solutions in various forms of the high-order dispersive cubic-quintic nonlinear Schrödinger equation are derived. These solutions have applications in engineering, nonlinear physics and fiber optics, providing insights into the physical nature of wave propagation in dispersive optics media. The results obtained form a basis for understanding complex physical phenomena in the described dynamical model. The computational approach employed is demonstrated to be straightforward, versatile, potent, and effective. Additionally, the presented solutions showcase various intriguing patterns, including kink-type periodic waves, combined bright-dark periodic waves, multipeak solitons, and breather-type waves. This diverse set of solutions contributes to the interpretation of the dynamical model, illustrating its complexity. Moreover, the simplicity and effectiveness of our computational technique make it applicable to solving similar models in physics and other fields of applied science.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5300-5314"},"PeriodicalIF":2.1,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380694","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":"Improved stability results for neural networks of neutral type with additive time-varying delays and Markovian jumping parameters","authors":"R. Sugumar,&nbsp;R. Agalya,&nbsp;D. Ajay","doi":"10.1002/mma.10597","DOIUrl":"https://doi.org/10.1002/mma.10597","url":null,"abstract":"<p>This paper investigates stability problem for neural networks of neutral type with additive time-varying delays and Markovian jump parameters. By constructing an improved Lyapunov-Krasovskii functional with triple and four integral terms and applying the free matrix variables in approximating certain integral quadratic terms, applying the free matrix variables in approximating certain integral quadratic terms, we derived the stability condition in terms of linear matrix inequalities (LMIs). Two numerical examples are provided to show the effectiveness of the proposed method. The obtained results are compared with the existing results to show the conservativeness.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5187-5201"},"PeriodicalIF":2.1,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380308","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":"Mild solution of semilinear evolution equation on an unbounded interval and its application in second-order hyperbolic PDE","authors":"Effat Gohari Moghaddam,&nbsp;Mahnaz Khanehgir,&nbsp;Hojjatollah Amiri Kayvanloo,&nbsp;Reza Allahyari","doi":"10.1002/mma.10584","DOIUrl":"https://doi.org/10.1002/mma.10584","url":null,"abstract":"<p>The aim of this paper is to discuss the existence of the mild solution for the infinite system of second-order hyperbolic PDE with boundary/initial value problem with nonlocal condition on an unbounded interval of the shape \u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4924-4936"},"PeriodicalIF":2.1,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380305","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 for a nonlocal semilinear pseudo-parabolic \u0000p-Laplacian type equation","authors":"Changping Xie,&nbsp;Shaomei Fang","doi":"10.1002/mma.10599","DOIUrl":"https://doi.org/10.1002/mma.10599","url":null,"abstract":"<p>In this paper, a nonlocal semilinear pseudo-parabolic \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math>-Laplacian type equation is considered, and finite time blow-up of solution with different initial energy is proved. More precisely, the upper bound for the blow-up time of solution with subcritical initial energy is established by potential well method and concavity argument. When the initial energy is supercritical, we prove the finite time blow-up of solution and obtain the upper bound for the blow-up time by different invariant set and concavity inequality. Moreover, by constructing a new control functional and providing careful estimates, the lower bound for the blow-up time of solution is given.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5235-5243"},"PeriodicalIF":2.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143381027","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":"Finite-time output feedback preview control for linear parameter-varying systems with input saturation","authors":"Li Li,&nbsp;Yanrong Lu,&nbsp;Yaofeng Zhang","doi":"10.1002/mma.10607","DOIUrl":"https://doi.org/10.1002/mma.10607","url":null,"abstract":"<p>This paper investigates the finite-time preview saturated control problem for linear parameter-varying systems with input saturation. The external disturbances and input saturation, previewable reference signals, and parameter variations are considered simultaneously. First, using the error system method, we construct an augmented error system with previewed information. This transforms the finite-time preview saturated control problem into a finite-time stabilization problem. Next, static output-feedback controllers are used to guarantee the finite-time boundedness of the closed-loop system. Sufficient conditions guarantee the existence of the desired controllers are obtained using linear matrix inequalities. At last, we use a numerical simulation to show the proposed design method's effectiveness.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5337-5353"},"PeriodicalIF":2.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143381028","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":"Local hyperthermic treatment of an advanced in vivo malignant tumor: A compartmental cum mathematical model","authors":"Saqib Mubarak","doi":"10.1002/mma.10608","DOIUrl":"https://doi.org/10.1002/mma.10608","url":null,"abstract":"<p>Hyperthermia, also called as thermal ablation, is used to treat some advanced cancers. Numerous clinical trials indicate that hyperthermia, when combined with therapies like radiation and chemotherapy, can reduce tumor size and potentially enhance their ability to eradicate cancerous cells. Hence, it is of utmost importance to study the behavior and transmission dynamics of in vivo malignant tumors subjected to hyperthermia. To this purpose, a mathematical model has been formulated, primarily based on the reaction–diffusion equation, imposed with suitable initial and boundary conditions. As the advanced tumors usually consist of five layers, the domain is discretized into five compartments. The model is then solved analytically using the eigenvalue expansion method to determine the tumor cell volume profiles, in the presence and absence of hyperthermia. The main foci of the developed model are the discretization of the domain, variable nature of various physiological parameters involved, and its analytical solution, thereby aiming at strengthening the novelties of the present work. The model outcome and simulations obtained are compared with the previously published/clinical results to prove the validity and feasibility of the proposed work. This work is expected to provide an optimum mathematical model utilizing best mathematical techniques that can greatly aid researchers and biologists in the field of oncology to streamline the process and reduce costs associated with cancer treatment.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5354-5364"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380921","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":"Rotating micropolar hybrid nanofluid: Exothermic/endothermic effects and waste discharge on exponential sheet","authors":"Kajal Bhaskar,&nbsp;Kalpna Sharma,&nbsp;Khushbu Bhaskar","doi":"10.1002/mma.10596","DOIUrl":"https://doi.org/10.1002/mma.10596","url":null,"abstract":"<p>This research offers a comprehensive investigation into the steady-state, three-dimensional flow of an incompressible hybrid nanofluid over a bi-directionally stretching exponential sheet. A central aspect of the study is the behavior of rotating micropolar fluids within a Darcy-Forchheimer porous medium, enhanced by the inclusion of electromagnetic forces. The effects of embedding nanoparticles \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mi>TiO</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow></math> and \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mtext>CoFe</mtext>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow></math> in a water-based fluid are explored to reveal their influence on fluid motion and heat transfer. The thermal dynamics are scrutinized, with particular emphasis on the roles of heat absorption and viscous dissipation. Moreover, this study incorporates both endothermic and exothermic reactions in radiative flows, alongside the impact of Soret and Dufour diffusion effects. The discharge of wastewater is a critical issue in environmental management and industrial applications, underscoring the need for rigorous regulation to prevent water pollution and ensure adherence to environmental standards. This research addresses the non-Newtonian flow resulting from wastewater discharge, incorporating Arrhenius activation energy in the analysis. Furthermore, the behavior of microorganisms within the flow is studied under velocity slip conditions and a range of convective boundary conditions. Through the application of similarity transformations, the governing differential equations are derived and solved numerically using MATLAB's bvp4c solver, with results depicted through detailed graphical analysis to illustrate the fluid's complex behavior. The heat transfer rate gets reduced by 1.96% with the enhancement in the Eckert number.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5154-5186"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380915","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":"Analytical approach in designing PID controller for complex fractional order transfer function","authors":"Uğur Demiroğlu,&nbsp;Bilal Şenol,&nbsp;Radek Matušů","doi":"10.1002/mma.10579","DOIUrl":"https://doi.org/10.1002/mma.10579","url":null,"abstract":"<p>The study focuses on the fractional complex order plant model, which has gained popularity in applied mathematics, physics, and control systems. A significant contribution of this research lies in discussing the physical phenomena associated with complex plant models and their impact on system stability and robustness. The main purpose of the method presented in this paper is to tune the controller parameters to ensure the stability and robustness of the system. There are methods presented in the literature for this purpose. One of these methods is to keep the phase curve in the system frequency response flat within a certain range. However, this process is based on equating the derivative of the phase value to zero at a certain frequency and adds great mathematical complexity to the calculations. In this study, reliable analytical formulas are presented for the same purpose using a graphical approach. Since the fractional complex order plant model represents the most general mathematical form, it enables easy creation of other plant models, including integer order and fractional order plant. The reason why this plant is chosen is that this structure can be named as the universal plant, which all other structures can be built by making little variations. For instance, a transfer function having integer, real and/or complex number coefficients and/or orders can be obtained by proper determination of the parameters of the universal plant. A time delay can also be added towards researcher's desire. The main inspiration comes from studying on an inclusive plant. The method in this paper intends to tune the well-known classical Proportional Integral Derivative controller. Thus, effectiveness of the integer order controller on various plants will be shown. This approach provides analytical calculation equations for the physical modifications of plants with integer, fractional, and/or complex coefficients and/or orders. The effectiveness of the method is demonstrated visually with different examples that include these different possible situations. The results observed in the changes of the parameters in the transfer functions were also examined. Thus, pros and cons of the variations of integer, fractional, and complex numbers on system parameters have been shown.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4862-4880"},"PeriodicalIF":2.1,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10579","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An algorithm with feasible inexact projections for solving constrained generalized equations","authors":"Samundra Regmi,&nbsp;Ioannis K. Argyros,&nbsp;Santhosh George","doi":"10.1002/mma.10567","DOIUrl":"https://doi.org/10.1002/mma.10567","url":null,"abstract":"<p>The goal of this article is to design a more flexible algorithm than the ones used previously for solving constrained generalized equations. It turns out that the new algorithm even if specialized provides a finer error analysis with advantages: larger radius of convergence; tighter upper error bounds on the distances; and a more precise information on the isolation of the solution. Moreover, the same advantages exist even if the generalized equation reduces to a nonlinear equation. These advantages are obtained under the same computational cost, since the new parameters and majorant functions are special cases of the ones used in earlier studies. Applications complement the theoretical results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4637-4648"},"PeriodicalIF":2.1,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380805","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":"Numerical ergodicity of a full-discrete exponential Euler scheme for stochastic Burgers–Huxley equation","authors":"Xue Wang,&nbsp;Shang Wu,&nbsp;Jianhua Huang,&nbsp;Jiaxing Zheng","doi":"10.1002/mma.10598","DOIUrl":"https://doi.org/10.1002/mma.10598","url":null,"abstract":"<p>In this paper, we mainly complete the research on approximate study of invariant measures for one-dimensional stochastic Burgers–Huxley equations driven by additive Gaussian noise. A fully discretization scheme is proposed based on the spectral Galerkin method and the exponential Euler scheme in both spatial and temporal directions, respectively. Moreover, we establish the unique ergodicity for both the spatial semi-discretization and the full discretization of numerical solutions, along with providing rigorous error estimations for invariant measures under approximate conditions. Some numerical experiments are presented to verify the theoretical findings.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"5202-5234"},"PeriodicalIF":2.1,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380803","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}