Mathematical Methods in the Applied Sciences最新文献

{"title":"On Some Inverse Problems for a Degenerate Parabolic Equation With Multiple Involution","authors":"Batirkhan Turmetov,&nbsp;Ainur Shalkhar","doi":"10.1002/mma.70583","DOIUrl":"https://doi.org/10.1002/mma.70583","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, initial-boundary value problems for a nonlocal analogue of a degenerate parabolic equation are considered. The authors study the inverse problems where it is necessary to determine not only a solution to the equation, but also a function in its right-hand side. In the framework of this research theorems on the existence and uniqueness of solutions to these problems are proved.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10239-10252"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343160","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 Intra-Layer and Inter-Layer Synchronization of Fractional-Order Multi-Layer Networks With Time-Varying Delays","authors":"Qiu Peng,&nbsp;Manchun Tan","doi":"10.1002/mma.70585","DOIUrl":"https://doi.org/10.1002/mma.70585","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper focuses on the finite-time intra-layer synchronization (FTALS) and finite-time inter-layer synchronization (FTRLS) of fractional-order multi-layer networks (FOMLNs) with time-varying delays. To begin, two forms of continuous control schemes with time-varying delays are proposed: State feedback control and fractional-order adaptive control. Following that, based on the finite-time stability theory and utilizing fractional-order differential inequalities and other inequality approaches, several new sufficient conditions for intra-layer synchronization (ALS) and inter-layer synchronization (RLS) of FOMLNs in finite time are given. Furthermore, the control gains here can be widely selected, and the upper bounds of the settling times for FTALS and FTRLS are explicitly derived in terms of the control gains and network parameters. Lastly, the viability of the theoretical results is demonstrated by two numerical examples.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10108-10132"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343254","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":"Projective Synchronization of Fractional-Order BAM Clifford-Valued Delayed Memristive Neural Networks: An Inner Product-Based Inequality","authors":"N. Manoj,&nbsp;R. Sriraman","doi":"10.1002/mma.70592","DOIUrl":"https://doi.org/10.1002/mma.70592","url":null,"abstract":"<div>\u0000 \u0000 <p>This article is devoted to solving the global Mittag-Leffler (GML) projective synchronization problem of a new type of fractional-order BAM memristive Clifford-valued delayed neural networks (FOBAMMCLVDNNs) using novel inner product-based inequalities. Unlike existing studies that are based on decomposition methods, we establish novel inner product-based inequalities using the sign function and the norm of Clifford numbers, allowing us to analyze the dynamics of FOBAMMCLVDNNs without decomposing them into real-valued systems. Through the established inequalities, the lexicographical order method, and the construction of two new general Lyapunov functions, we obtain some new criteria for the GML projective synchronization problem of FOBAMMCLVDNNs. The derived results include GML complete synchronization and GML anti-synchronization of FOBAMMCLVDNNs as special cases. To validate the effectiveness of the proposed synchronization criteria, numerical simulations for different cases are presented, accompanied by graphical analysis. Additionally, the obtained results are utilized to develop an image encryption algorithm, and the experimental results verify the proposed encryption algorithm's efficiency for secure communication applications.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10378-10416"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343203","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":"Thermal Planar and Radial Free Jets for An Ostwald-de Waele Fluid With Shear-Rate Dependent Thermal Diffusivity","authors":"Avnish Bhowan Magan,&nbsp;Rehana Naz","doi":"10.1002/mma.70599","DOIUrl":"https://doi.org/10.1002/mma.70599","url":null,"abstract":"&lt;p&gt;The planar and radial thermal free jets for forced convection of a non-Newtonian power-law fluid are investigated. The thermal diffusivity is dependent on the shear-rate and is not a constant. The flow in planar and radial thermal free jets is governed by the momentum, continuity and energy balance equations. In the stream-function formulation, the governing equations reduce to a system of two coupled partial differential equations for the stream function and temperature. Conservation laws for this system are obtained using the multiplier method. Group invariant solutions for the planar and radial thermal free jets are derived by a Lie point symmetry associated with the conserved vectors. Analytical solutions for the velocity components and temperature function are found in parametric form. It is shown that solutions are only admissible in the representative range &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ frac{1}{2}&lt;n&lt;infty $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For dilitant fluids, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ n&gt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the jets are characterised by a boundary curve but not for pseudoplastic fluids, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ frac{1}{2}&lt;n&lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and Newtonian fluids, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ n=1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. It is shown that the jet flow characteristics depend on the flow index, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;a","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10312-10333"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70599","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343150","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":"A Spectral Dai–Liao Conjugate Gradient Method With Strong Theoretical Guarantees for Image Restoration and Machine Learning","authors":"Jiang Xiong,&nbsp;Wanting Huang,&nbsp;Jinkui Liu","doi":"10.1002/mma.70589","DOIUrl":"https://doi.org/10.1002/mma.70589","url":null,"abstract":"<div>\u0000 \u0000 <p>Based on a class of adaptive Dai–Liao parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$$ t $$</annotation>\u0000 </semantics></math> (4OR-Q J Oper Res, 2017, 15: 85–92), this paper proposes a novel Dai–Liao parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$$ t $$</annotation>\u0000 </semantics></math> with an explicit upper bound by minimizing the spectral condition number of the search direction matrix, significantly enhancing algorithmic stability. To further strengthen theoretical guarantees, a spectral parameter is designed to ensure the Dai–Liao conjugate gradient method (DL-CGM) with sufficient descent property under the standard Wolfe conditions. Moreover, the global convergence is established for general functions under mild conditions. Numerical experiments on unconstrained optimization problems, image restoration and machine learning demonstrate the effectiveness and applicability of the proposed method compared to existing CGMs.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 10","pages":"10347-10365"},"PeriodicalIF":2.0,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148343202","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 9","pages":"8625-8631"},"PeriodicalIF":1.8,"publicationDate":"2026-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148083118","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":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 8","pages":"7229-7235"},"PeriodicalIF":1.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148079779","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":"Existence of Traveling Wave Solutions for the Perturbed Extended Kadomtsev–Petviashvili Equation","authors":"Bo Yan,&nbsp;Yezhou Li,&nbsp;Yao Qi,&nbsp;Yu Tian","doi":"10.1002/mma.70379","DOIUrl":"https://doi.org/10.1002/mma.70379","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we apply geometric singular perturbation theory and Melnikov's method to the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(2+1right) $$</annotation>\u0000 </semantics></math>-dimensional extended Kadomtsev–Petviashvili (eKP) equation with singular perturbations. For the first time, we rigorously establish the existence of solitary wave solutions under KS-type perturbations, proving that two distinct solitary waves with speeds <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {c}_0 $$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {c}_1 $$</annotation>\u0000 </semantics></math> persist. These theoretical results are supported by numerical simulations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 7","pages":"6101-6111"},"PeriodicalIF":1.8,"publicationDate":"2026-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147685924","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":"Uncertainty Principles for Quaternion Fourier Transform and Quaternion \u0000 \u0000 \u0000 K\u0000 \u0000 $$ mathbf{K} $$\u0000 -Ambiguity Function","authors":"Ping Liang,&nbsp;Pei Dang,&nbsp;Weixiong Mai","doi":"10.1002/mma.70388","DOIUrl":"https://doi.org/10.1002/mma.70388","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we obtain a sharper Heisenberg-Pauli-Weyl uncertainty principle for quaternion Fourier transforms, which is also generalized partially to the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^p $$</annotation>\u0000 </semantics></math> case with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>≤</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ 1le ple 2 $$</annotation>\u0000 </semantics></math>. In addition, we introduce the so-called quaternion <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbf{K} $$</annotation>\u0000 </semantics></math>-ambiguity function, and obtain related Heisenberg-Pauli-Weyl uncertainty principles for this generalized ambiguity function.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 7","pages":"6272-6299"},"PeriodicalIF":1.8,"publicationDate":"2026-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686073","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":"Exploring Nonlinear Dynamics in Fluid Mechanics: Bifurcation, Chaos, and Soliton Analysis","authors":"Muhammad Raheel,&nbsp;Asim Zafar","doi":"10.1002/mma.70383","DOIUrl":"https://doi.org/10.1002/mma.70383","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper reveals a nonlinear new dissipative Boussinesq model in a fluid mechanism system. This model is obtained from the quasi-geostrophic barotropic potential velocity equation. We use a fractional derivative to improve accuracy as well as understand the dynamics of the model. It describes the nonlinear Rossby waves in the atmosphere. By utilizing the modified simplest equation method, we investigate the distinct kinds of exact wave solutions involving trigonometric, hyperbolic, and rational functions. To obtain and verify the solutions, we use the Mathematica software. We demonstrate the obtained solutions through two-dimensional, three-dimensional, and contour graphs by using the Mathematica tool. The main contribution of this paper is to analyze the qualitative analysis, including modulation instability, bifurcation analysis, chaotic behavior, and sensitivity nature. We explore the important characteristics of chaos through two-dimensional (2-D) phase portraits, three-dimensional (3-D) phase portraits, Poincaré sections, time series, and Lyapunov exponents. At the end, the gained solutions are fruitful in different areas, like oceanography, fluid dynamics, coastal engineering, and many others.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 7","pages":"6158-6179"},"PeriodicalIF":1.8,"publicationDate":"2026-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686773","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}