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Finite-time stability in measure for nabla uncertain discrete linear fractional order systems 不确定离散线性分数阶系统的有限时间测度稳定性
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-07-06 DOI: 10.1007/s40096-022-00484-y
Qinyun Lu, Yuanguo Zhu

With the development of mathematical theory, fractional order equation is becoming a potential tool in the context of neural networks. This paper primarily concerns with the stability for systems governed by the linear fractional order uncertain difference equations, which may properly portray neural networks. First, the solutions of these linear difference equations are provided. Secondly, the definition of finite-time stability in measure for the proposed systems is introduced. Furthermore, some sufficient conditions checking for it are achieved by the property of fractional order difference and uncertainty theory. Besides, the relationship between finite-time stability almost surely and in measure is discussed. Finally, some numerical examples are analysed by employing the proposed results.

随着数学理论的发展，分数阶方程正在成为神经网络研究的一个潜在工具。本文主要研究由线性分数阶不确定差分方程控制的系统的稳定性，它可以很好地描述神经网络。首先，给出了这些线性差分方程的解。其次，给出了系统有限时间测度稳定性的定义。并利用分数阶差分的性质和不确定性理论，给出了检验其正确性的充分条件。此外，还讨论了有限时间稳定与测度稳定之间的关系。最后，对数值算例进行了分析。
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引用次数: 0
Interpolative multivalued $$alpha _{*}$$-dominated contractive functions in dislocated b-metric spaces and some fixed point results 位错b-度量空间中的插值多值$$alpha _{*}$$ -主导压缩函数及一些不动点结果
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-07-03 DOI: 10.1007/s40096-022-00480-2
A. Shoaib, Usman Mir
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引用次数: 0
Existence of solutions for the nonlinear integro-differential system 非线性积分-微分系统解的存在性
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-06-29 DOI: 10.1007/s40096-022-00479-9
Chenkuan Li, R. Saadati, F. Mottaghi, M. Ghaemi
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引用次数: 0
A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines 非线性Burgers方程的四次三角张力b样条计算方法
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-06-27 DOI: 10.1007/s40096-022-00481-1
Gulsemay Yigit, Ozlem Ersoy Hepson, Tofigh Allahviranloo

This work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear Burgers’ equation. The computational scheme is constructed by a discretized space-time hybrid approach using B-spline functions. This methodology produces a system of time-dependent differential equations which is integrated by finite elements technique. The experimental cases including graphical patterns of each wave interaction are simulated by the current computational algorithm. In addition, the method establishes the capacity to provide highly efficient solutions with relative ease of computation. Investigation of the stability analysis shows that the current computational method serves an unconditional stable numerical scheme.

本文提出了一种以四次三角基函数为重点的求非线性Burgers方程数值解的有限元方法。计算方案采用b样条函数的离散时空混合方法。这种方法产生了一个由有限单元技术集成的时变微分方程系统。用现有的计算算法模拟了包括各波相互作用图形的实验案例。此外，该方法建立了提供相对易于计算的高效解的能力。对稳定性分析的研究表明，目前的计算方法适用于无条件稳定的数值格式。
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引用次数: 0
Applications of Sine–Cosine wavelets method for solving the generalized Hirota–Satsuma coupled KdV equation 正弦余弦小波方法在求解广义Hirota-Satsuma耦合KdV方程中的应用
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-06-26 DOI: 10.1007/s40096-022-00477-x
N. Azizi, R. Pourgholi
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引用次数: 2
On the modeling and numerical discretizations of a chaotic system via fractional operators with and without singular kernels 含和不含奇异核分数算子的混沌系统建模与数值离散
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-06-24 DOI: 10.1007/s40096-022-00478-w
N. Sene
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引用次数: 1
Correction to: Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem 修正:二维非线性最优控制问题的鲁棒二元多项式格式与收敛分析
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-06-07 DOI: 10.1007/s40096-022-00476-y
Asiyeh Ebrahimzadeh, Samaneh Panjeh Ali Beik
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引用次数: 0
Integration of the RLW equation using higher-order predictor–corrector scheme and quintic B-spline collocation method 采用高阶预测校正格式和五次b样条配点法对RLW方程进行积分
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-05-31 DOI: 10.1007/s40096-022-00475-z
Bülent Saka, İdris Dağ, Ozlem Ersoy Hepson

Solitary wave solutions are studied by way of the regularized long wave (RLW) equation. RLW equation is fully integrated by using combination of the quintic collocation method and predictor–corrector method. The implementation of the new presented method is shown in the RLW equation. Accuracy of numerical solutions of the RLW equation is seen to be increased by employing the predictor–corrector time integrator for the collocation method. Comparison of results is done with some earlier prosperous methods. Four problems are tested to show validity and efficiency of the techniques.

利用正则化长波方程研究了孤波解。采用五次配点法和预测校正法相结合的方法对RLW方程进行了充分的积分。新方法的实现用RLW方程表示。采用预测-校正时间积分器的配置方法可以提高RLW方程数值解的精度。并与一些较早的方法进行了比较。通过对四个问题的测试，验证了该方法的有效性和有效性。
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引用次数: 0
Computational algorithm for financial mathematical model based on European option 基于欧式期权的金融数学模型的计算算法
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-05-30 DOI: 10.1007/s40096-022-00474-0
Nikhil Srivastava, Aman Singh, V. Singh
{"title":"Computational algorithm for financial mathematical model based on European option","authors":"Nikhil Srivastava, Aman Singh, V. Singh","doi":"10.1007/s40096-022-00474-0","DOIUrl":"https://doi.org/10.1007/s40096-022-00474-0","url":null,"abstract":"","PeriodicalId":48563,"journal":{"name":"Mathematical Sciences","volume":"53 1","pages":"467 - 490"},"PeriodicalIF":2.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81157001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem 二维非线性最优控制问题的鲁棒二元多项式格式及其收敛分析
IF 2 4区 数学 Q1 MATHEMATICS
Mathematical Sciences
Pub Date : 2022-05-23 DOI: 10.1007/s40096-022-00473-1
Asiyeh Ebrahimzadeh, Samaneh Panjeh Ali Beik
{"title":"Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem","authors":"Asiyeh Ebrahimzadeh, Samaneh Panjeh Ali Beik","doi":"10.1007/s40096-022-00473-1","DOIUrl":"https://doi.org/10.1007/s40096-022-00473-1","url":null,"abstract":"","PeriodicalId":48563,"journal":{"name":"Mathematical Sciences","volume":"40 1","pages":"325 - 335"},"PeriodicalIF":2.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89666394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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