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Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions 具有多点和多期积分边界条件的六阶边界值问题的可解性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-18 DOI: 10.1002/mma.10492
Faouzi Haddouchi, Nourredine Houari
{"title":"Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions","authors":"Faouzi Haddouchi, Nourredine Houari","doi":"10.1002/mma.10492","DOIUrl":"https://doi.org/10.1002/mma.10492","url":null,"abstract":"This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"28 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258431","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}
引用次数: 0
Two geometrical invariants for three‐dimensional systems 三维系统的两个几何不变式
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-18 DOI: 10.1002/mma.10491
Aimin Liu, Yongjian Liu, Xiaoting Lu
{"title":"Two geometrical invariants for three‐dimensional systems","authors":"Aimin Liu, Yongjian Liu, Xiaoting Lu","doi":"10.1002/mma.10491","DOIUrl":"https://doi.org/10.1002/mma.10491","url":null,"abstract":"The subject of KCC theory is a second‐order ordinary differential equation, it is sometimes difficult to convert the high dimensional system into an equivalent second‐order system because of the analytical requirements of KCC theory. By means of the Euler‐Lagrange extension of a flow on a Riemannian manifold, this paper gives five geometric invariants of some three‐dimensional systems with great convenience, and focus on the analysis of two of them. The results show that the hyperbolic equilibria corresponding to the seven standard forms of three‐dimensional linear systems are Jacobi unstable. This is completely different from what we got before in two‐dimensional systems, where Jacobi stable and Jacobi unstable correspond to focus and node, respectively. All equilibria of classical Lü chaotic system and Yang‐Chen chaotic system are Jacobi unstable. Meanwhile, in three‐dimensional linear case, the torsion tensors at any point of the trajectory are identically equal to zero, but the two nonlinear systems have nonzero torsion tensors components.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258430","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}
引用次数: 0
Infinitely of solutions for fractional κ(ξ)$$ kappa left(xi right) $$‐Kirchhoff equation in Hκ(ξ)ϖ,ν;μ(Λ)$$ {mathcal{H}}_{kappa left(xi right)}^{varpi, nu; mu}left(Lambda right) $$ 在Hκ(ξ)ϖ,ν中的分式κ(ξ)$$ {{kappa（左）（西）（右）}$$-基尔霍夫方程的无限解μ（Λ）$$ {{mathcal{H}}_{kappa（左）（西）（右）}^{varpi, nu;mu}（左）（λ）$$
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI: 10.1002/mma.10477
Abdelhakim Sahbani, J. Vanterler da C. Sousa
{"title":"Infinitely of solutions for fractional κ(ξ)$$ kappa left(xi right) $$‐Kirchhoff equation in Hκ(ξ)ϖ,ν;μ(Λ)$$ {mathcal{H}}_{kappa left(xi right)}^{varpi, nu; mu}left(Lambda right) $$","authors":"Abdelhakim Sahbani, J. Vanterler da C. Sousa","doi":"10.1002/mma.10477","DOIUrl":"https://doi.org/10.1002/mma.10477","url":null,"abstract":"This work aims to develop the variational framework for some Kirchhoff problems involving the ‐Hilfer operator. Precisely, we use the symmetric mountain pass theorem to prove the existence of unfairly of nontrivial solutions. Further, we research the results from the theory of variable exponent Sobolev spaces and from the theory of ‐fractional space .","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"103 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258434","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}
引用次数: 0
An approximate solution for stochastic Fitzhugh–Nagumo partial differential equations arising in neurobiology models 神经生物学模型中出现的随机 Fitzhugh-Nagumo 偏微分方程的近似解法
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI: 10.1002/mma.10471
D. Uma, H. Jafari, S. Raja Balachandar, S. G. Venkatesh, S. Vaidyanathan
{"title":"An approximate solution for stochastic Fitzhugh–Nagumo partial differential equations arising in neurobiology models","authors":"D. Uma, H. Jafari, S. Raja Balachandar, S. G. Venkatesh, S. Vaidyanathan","doi":"10.1002/mma.10471","DOIUrl":"https://doi.org/10.1002/mma.10471","url":null,"abstract":"In this paper, approximate solutions for stochastic Fitzhugh–Nagumo partial differential equations are obtained using two‐dimensional shifted Legendre polynomial (2DSLP) approximation. The problem's suitability and solvability are confirmed. The convergence analysis for the proposed methodology and the error analysis in the norm are carried out. Using Maple software, an algorithm is created and implemented to arrive at the numerical solution. The solution thus obtained is compared with the exact solution and the solution obtained using the explicit order RK1.5 method.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"18 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258507","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}
引用次数: 0
Similarity and consimilarity of hyper‐dual generalized quaternions 超二元广义四元数的相似性和相通性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI: 10.1002/mma.10488
Yasemin Alagöz, Gözde Özyurt
{"title":"Similarity and consimilarity of hyper‐dual generalized quaternions","authors":"Yasemin Alagöz, Gözde Özyurt","doi":"10.1002/mma.10488","DOIUrl":"https://doi.org/10.1002/mma.10488","url":null,"abstract":"The aim of this paper is to investigate similarity and consimilarity of hyper‐dual generalized quaternions and their matrices. For this purpose, we give different conjugates according to the generalized quaternionic units . We present ‐consimilarity of hyper‐dual generalized quaternions and their matrices except hyper‐dual ‐quaternions. For the generalization consisting of hyper‐dual coefficients quaternion and split quaternion, we search ‐consimilarity and ‐consimilarity with the help of ‐conjugate and ‐conjugate. We also give ‐coneigenvalues and ‐coneigenvectors of the matrices of these generalizations. In addition, we examine right coneigenvalue problem in generalized quaternion matrices for real and split quaternions. The complex matrix representation obtained through the complex adjoint matrix representation of this generalization is introduced, and its properties are presented. Besides, we give algebraic methods for the concept of right coneigenvalues and coneigenvectors for matrices, which are the generalization of real quaternion and split quaternion.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"81 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258432","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}
引用次数: 0
American barrier swaption pricing problem of exponential Ornstein–Uhlenbeck model in uncertain financial market
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-16 DOI: 10.1002/mma.10450
Dongao Li, Jiarui Jiang, Lifen Jia
{"title":"American barrier swaption pricing problem of exponential Ornstein–Uhlenbeck model in uncertain financial market","authors":"Dongao Li,&nbsp;Jiarui Jiang,&nbsp;Lifen Jia","doi":"10.1002/mma.10450","DOIUrl":"https://doi.org/10.1002/mma.10450","url":null,"abstract":"<p>Barrier swaption is a financial derivative that integrates aspects of a traditional swaption with the distinctive features of a barrier option. In this study, based on the premise that floating interest rates obey the exponential Ornstein–Uhlenbeck model, we derive the pricing formulas for two types of American barrier swaptions for payer and receiver, respectively, and design corresponding algorithms. In the empirical part, we select the Hong Kong Interbank Offer Rate (HIBOR) data from the real financial market to estimate the parameters of the uncertain differential equation that governs floating interest rates and test the hypothesis. It is worth noting that through rigorous hypothesis testing, we verify the applicability of the equation. Finally, we use the actual estimated parameters combined with the uncertain differential equation to carry out a range of numerical experiments, which provides a strong support for the pricing of American barrier swaptions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2545-2560"},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861534","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}
引用次数: 0
Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems 两个混合系统半离散化方案的统一指数稳定性近似值
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-14 DOI: 10.1002/mma.10484
Lu Zhang, Fu Zheng, Sizhe Wang, Zhongjie Han
{"title":"Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems","authors":"Lu Zhang, Fu Zheng, Sizhe Wang, Zhongjie Han","doi":"10.1002/mma.10484","DOIUrl":"https://doi.org/10.1002/mma.10484","url":null,"abstract":"The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258437","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}
引用次数: 0
Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles 克利福德值线性小波变换和相应的不确定性原理
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10468
Shahbaz Rafiq, Mohammad Younus Bhat
{"title":"Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles","authors":"Shahbaz Rafiq, Mohammad Younus Bhat","doi":"10.1002/mma.10468","DOIUrl":"https://doi.org/10.1002/mma.10468","url":null,"abstract":"The present article establishes a novel transform known as Clifford‐valued linear canonical wavelet transform which is intended to represent ‐dimensional Clifford‐valued signals at various scales, locations, and orientations. The suggested transform is capable of representing signals in the Clifford domain in addition to inheriting the characteristics of the Clifford wavelet transform. In the beginning, we demonstrate the proposed transform by the help of ‐dimensional difference of Gaussian wavelets. We then establish the fundamental properties of the proposed transform like Parseval's formula, inversion formula, and characterization of its range using Clifford linear canonical transform and its convolution. To conclude our work, we derive an analog of Heisenberg's and local uncertainty inequalities for the proposed transform.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"3 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220068","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}
引用次数: 0
Pattern dynamics in a water–vegetation model with cross‐diffusion and nonlocal delay 具有交叉扩散和非局部延迟的水-植被模型中的模式动力学
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10480
Gaihui Guo, Jing You, Khalid Ahmed Abbakar
{"title":"Pattern dynamics in a water–vegetation model with cross‐diffusion and nonlocal delay","authors":"Gaihui Guo, Jing You, Khalid Ahmed Abbakar","doi":"10.1002/mma.10480","DOIUrl":"https://doi.org/10.1002/mma.10480","url":null,"abstract":"In semiarid areas, the positive feedback effect of vegetation and soil moisture plays an indispensable role in the water absorption process of plant roots. In addition, vegetation can absorb water through the nonlocal interaction of roots. Therefore, in this article, we consider how the interactions between cross‐diffusion and nonlocal delay affect vegetation growth. Through mathematical analysis, the conditions for the occurrence of the Turing pattern in the water–vegetation model are obtained. Meanwhile, using the multi‐scale analysis method, the amplitude equation near the Turing bifurcation boundary is obtained. By analyzing the stability of the amplitude equation, the conditions for the appearance of Turing patterns such as stripes, hexagons, and mixtures of stripes and hexagons are determined. Some numerical simulations are given to illustrate the analytical results, especially the evolution processes of vegetation patterns depicted under different parameters.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"29 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220216","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}
引用次数: 0
Viscoelasticity, logarithmic stresses, and tensorial transport equations 粘弹性、对数应力和张量传输方程
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10469
Gennaro Ciampa, Giulio G. Giusteri, Alessio G. Soggiu
{"title":"Viscoelasticity, logarithmic stresses, and tensorial transport equations","authors":"Gennaro Ciampa, Giulio G. Giusteri, Alessio G. Soggiu","doi":"10.1002/mma.10469","DOIUrl":"https://doi.org/10.1002/mma.10469","url":null,"abstract":"We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally belong to a multiplicative group of linear transformations, to stresses, that are additive elements of a linear space of tensors. As regards the viscous stresses, we simply assume a Newtonian constitutive law, but the presence of elasticity and plastic relaxation makes the materials non‐Newtonian. Our aim is to discuss the existence of weak solutions for the corresponding systems of partial differential equations in the nonlinear large‐deformation regime. The main difficulties arise in the analysis of the transport equations necessary to describe the evolution of tensorial measures of strain. For the solid model, we only need to consider the equation for the left Cauchy–Green tensor, while for the fluid model, we add an evolution equation for the elastically‐relaxed strain. Due to the tensorial nature of the fields, available techniques cannot be applied to the analysis of such transport equations. To cope with this, we introduce the notion of charted weak solution, based on non‐standard a priori estimates, that lead to a global‐in‐time existence of solutions for the viscoelastic models in the natural functional setting associated with the energy inequality.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"171 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220214","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}
引用次数: 0
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