Mathematical Methods in the Applied Sciences最新文献

{"title":"Exponential Decay Results of Solutions for a One-Dimensional Magnetizable Piezoelectric Beam System of Thermoelasticity of Type III With Strong Damping and a Strong Delay","authors":"Hassan Messaoudi,&nbsp;Sami Loucif,&nbsp;Salah Zitouni","doi":"10.1002/mma.70011","DOIUrl":"https://doi.org/10.1002/mma.70011","url":null,"abstract":"<div>\u0000 \u0000 <p>In this research work, we study a one-dimensional magnetizable piezoelectric beam system with strong damping and a strong delay acting on the heat equation, where the heat conduction is given by Green and Naghdi theory. First, we establish by exploiting the semigroup theory that the system is well-posed. Through the construction of an appropriate Lyapunov functional, we establish the exponential stability result for the solutions of the system. The exponential stability of the system's solutions is established under a pertinent assumption regarding the weight of the delay. This assumption posits that the damping effect through heat conduction is sufficiently potent to stabilize the system, even when a time delay is introduced. Importantly, the robustness of our result is noteworthy, as it does not hinge on any specific relationships among system parameters.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15236-15246"},"PeriodicalIF":1.8,"publicationDate":"2025-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242959","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 Dirichlet Problem for the One-Dimensional Rudin–Osher–Fatemi Functional","authors":"Piotr Rybka","doi":"10.1002/mma.70014","DOIUrl":"https://doi.org/10.1002/mma.70014","url":null,"abstract":"<div>\u0000 \u0000 <p>We provide a number of sufficient conditions for those minimizers of the one-dimensional Rudin–Osher–Fatemi functional that satisfy the Dirichlet data in the trace sense. For this purpose, we use results specific for the total variation flow. We also show a number of counterexamples.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15265-15277"},"PeriodicalIF":1.8,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243167","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":"Boundary Value Problem for a Degenerate Equation of Even Order With a Fractional Derivative in a Mixed Domain","authors":"B. Yu. Irgashev","doi":"10.1002/mma.70012","DOIUrl":"https://doi.org/10.1002/mma.70012","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, in a rectangular domain, we study a Dirichlet-type problem with gluing conditions for a degenerate high-order equation with fractional derivatives in the Riemann–Liouville sense of orders \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ alpha in left(1,2right) $$</annotation>\u0000 </semantics></math>, for \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>y</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$$ y&amp;gt;0 $$</annotation>\u0000 </semantics></math>, and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ beta in left(1,2right) $$</annotation>\u0000 </semantics></math>, for \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>y</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$$ y&amp;lt;0 $$</annotation>\u0000 </semantics></math>. A criterion for the uniqueness of the solution of the stated problem is given. Using asymptotic expansions for the Mittag–Leffler function and Bessel's inequality, sufficient conditions for the existence of a solution are found.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15247-15255"},"PeriodicalIF":1.8,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243168","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 Comprehensive Subclass of Bi-Univalent Functions Related to Imaginary Error Function Subordinate to Bernoulli Polynomials","authors":"Sondekola Rudra Swamy,&nbsp;Kala Venugopal","doi":"10.1002/mma.70007","DOIUrl":"https://doi.org/10.1002/mma.70007","url":null,"abstract":"<div>\u0000 \u0000 <p>Our investigation is motivated by the wide range of interesting and fruitful applications of special polynomials. Among these, Bernoulli polynomials have recently garnered attention in the study of bi-univalent function theory. In this article, we introduce and analyze a broad subclass of bi-univalent functions associated with the imaginary error function, governed by Bernoulli polynomials. We derive initial coefficient bounds for functions in this subclass and explore their properties in relation to the Fekete–Szegö inequality. Additionally, we discuss connections to previous research while highlighting several new results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15172-15178"},"PeriodicalIF":1.8,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243193","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":"Long-Time Behavior of a Generalized Semi-Markov Model of Population Dynamics","authors":"Katarzyna Pichór,&nbsp;Ryszard Rudnicki","doi":"10.1002/mma.70008","DOIUrl":"https://doi.org/10.1002/mma.70008","url":null,"abstract":"<div>\u0000 \u0000 <p>We present applications of some generalization of semi-Markov processes. The general model is described by a first-order partial differential equation with initial-boundary conditions. It covers a variety of biological models including those described by piecewise deterministic Markov processes as well as advanced stochastic hybrid systems. We construct a semigroup of positive operators on the space of integrable functions related to this model. We study long-time behavior of solutions of selected models: phenotypic models and a stochastic population growth model with disasters.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15179-15193"},"PeriodicalIF":1.8,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243140","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":"Multiple Normalized Solutions for a Class of Elliptic Equations With Mixed Fractional Laplacians","authors":"Ruibin Jiang,&nbsp;Qihuan Xie","doi":"10.1002/mma.70016","DOIUrl":"https://doi.org/10.1002/mma.70016","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this paper is to establish a multiplicity of normalized solutions for a class of nonlinear elliptic equations with mixed fractional Laplacians, which is driven by the superposition of Brownian and Lévy processes. This result complements some known results in the literature. In the process of our proof, we mainly apply the concentration compactness principle and the Lusternik–Schnirelmann theory to obtain the results mentioned in this paper.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15289-15299"},"PeriodicalIF":1.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243190","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 Existence and Uniqueness of Positive Solutions to Population Balance Models for Column Crystallizers","authors":"Elias G. Saleeby,&nbsp;Nima Rabiei","doi":"10.1002/mma.70032","DOIUrl":"https://doi.org/10.1002/mma.70032","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we prove the existence and uniqueness of positive/nonnegative solutions on \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left[0,infty right) $$</annotation>\u0000 </semantics></math> of population balance models for column crystallizers. These solutions represent the crystal size distributions in the stages of the column. We first investigate a system of ODEs model for a column with no particle agglomeration. Then we consider a system of integrodifferential equations (IDEs) model that accounts for particle agglomeration. In this case, we turn a boundary value problem for a Fredholm-Volterra system of IDEs into an initial value problem of Volterra type IDEs coupled with a system of algebraic equations. We obtain our results employing some algebraic facts along with the Brouwer and the Schauder's fixed point theorems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15523-15532"},"PeriodicalIF":1.8,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243135","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":"Investigating Pancreatic Cancer Dynamics Through Fractional Modeling With Caputo Derivative","authors":"Mihir Thakkar,&nbsp;Anil Chavada,&nbsp;Nimisha Pathak","doi":"10.1002/mma.70023","DOIUrl":"https://doi.org/10.1002/mma.70023","url":null,"abstract":"<div>\u0000 \u0000 <p>This research investigates the interplay among pancreatic cancer cells (PCCs), pancreatic stellate cells (PSC), effector cells, and both tumor-suppressing and tumor-promoting cytokines to better understand the dynamics of pancreatic cancer. Using the Caputo fractional derivative, the traditional model is transformed into a fractional-order framework while maintaining dimensional consistency in its equations. The study examines equilibrium points, with a specific focus on the tumor-free and high-tumor state, to evaluate local stability. The fixed-point theorem is applied to confirm the existence and uniqueness of solutions, and global stability is established through the Hyers–Ulam–Rassias method. Numerical simulations, carried out using the zwo-step Adams-Bashforth method across various fractional orders, unveil the system's complex behaviors. These results contribute to a deeper understanding of pancreatic cancer dynamics and provide meaningful insights into its underlying mechanisms.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15387-15399"},"PeriodicalIF":1.8,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243186","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 Solution of Zabolotskaya–Khokhlov Equation Using Differential Quadrature Method by Fourier and Lagrange Bases","authors":"A. Elmekawy,&nbsp;M. S. El-Azab,&nbsp;Atallah El-Shenawy","doi":"10.1002/mma.70005","DOIUrl":"https://doi.org/10.1002/mma.70005","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This manuscript provides a comprehensive investigation of the Zabolotskaya–Khokhlov (Z-K) equation, a nonlinear partial differential equation essential for modeling wave propagation in acoustics. The main goal is to formulate and assess a hybrid numerical approach that combines finite difference and differential quadrature techniques, utilizing both Fourier and Lagrange basis functions to improve accuracy and efficiency. The problem formulation commences with defining the parameters and physical meaning of the Z-K equation, succeeded by its discretization in both temporal and spatial domains utilizing the proposed hybrid methodology. We systematically investigate the application of the differential quadrature method for approximating spatial derivatives while utilizing the finite difference method for temporal discretization. The paper introduces a quasi-linearization technique based on Taylor expansion of the nonlinear temporal terms. This dual methodology facilitates a versatile and resilient handling of the nonlinear features of the Z-K equation. A comprehensive error analysis is performed, establishing limits on both temporal and spatial errors related to the numerical solutions. The results indicate that the hybrid approach markedly enhances accuracy relative to conventional methods, with error barriers determined through meticulous mathematical derivation and corroborated by numerical simulations. The proposed scheme provides an error estimate of orders \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝒪&lt;/mi&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ς&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;!&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;𝒪&lt;/mi&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15140-15150"},"PeriodicalIF":1.8,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242929","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":"Dynamic Analysis of Quaternion-Valued Memristive Neural Networks: A New Generalized Inequality","authors":"Chenyu Sun,&nbsp;Ruoxia Li,&nbsp;Zhengwen Tu","doi":"10.1002/mma.70013","DOIUrl":"https://doi.org/10.1002/mma.70013","url":null,"abstract":"<div>\u0000 \u0000 <p>The exponential stability and the synchronization of QMNN are considered in this article. First, a new exponentially stable definition is proposed, it effectively estimates the rate of convergence, and the neural networks can converge to the equilibrium point at any rate by modifying the controller. Then, a simple controller is proposed to achieve the synchronization goal by a new lemma generalized from Halanay inequality, and a set of improved conditions are presented to achieve the synchronization control. The theorems are verified by some simulations in the end. The conclusions obtained in this paper not only avoid considering the “magnitude” of quaternion but also give a more flexible criteria.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15256-15264"},"PeriodicalIF":1.8,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242924","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}