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Advances in the Theory of Nonlinear Analysis and its Application最新文献

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Stability of the program manifold of automatic indirect control systems taking into account the external load 考虑外部负荷的自动间接控制系统程序流形的稳定性
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-04-13 DOI: 10.31197/atnaa.1200890
S. Zhumatov, S. Mynbayeva
{"title":"Stability of the program manifold of automatic indirect control systems taking into account the external load","authors":"S. Zhumatov, S. Mynbayeva","doi":"10.31197/atnaa.1200890","DOIUrl":"https://doi.org/10.31197/atnaa.1200890","url":null,"abstract":"The problems of stability system that arises in the construction of different automatic systems of indirect control are considered. It is known that a given program is not always exactly performed, since there are always initial, constantly acting perturbations. \u0000Therefore, it is also reasonable to require the stability of the program manifold itself with respect to some function. In the first part, the stability being investigated of automatic indirect control systems with rigid and tachometric feedback. Necessary and sufficient conditions for the absolute stability of a program manifold are established separately. In the second part, the automatic systems of indirect control taking into account the external load are considered. The equations of the hydraulic actuator, taking into account the action of an external load, are presented in a convenient form for research. Then it reduces to studying the stability of the system of equations with respect to a given program manifold. By constructing LyapunovВ’s functions for the system in canonical form, sufficient conditions are obtained for the absolute stability of the program manifold. The results obtained can be used in the construction of stable automatic indirect control systems.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85882420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolative Contractive Results for $m$-Metric Spaces $m$-Metric空间的插值压缩结果
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-04-04 DOI: 10.31197/atnaa.1220114
{"title":"Interpolative Contractive Results for $m$-Metric Spaces","authors":"","doi":"10.31197/atnaa.1220114","DOIUrl":"https://doi.org/10.31197/atnaa.1220114","url":null,"abstract":"In this paper, we initiate the study of fixed points for \u0000interpolative mappings in $m$-metric spaces. We discuss three different \u0000cases: the sum of textquotedblleft interpolative exponents\" is less than, \u0000equal to or greater than 1. We support each of our result by examples in $m$% \u0000-metric spaces. In the last section, we obtain our results in $p$-metric \u0000spaces. Finally we note that \u0000our results generalize results of cite{EY}, cite{GH} and cite{K} from ordinary metric to $m$- and $p$-metrics.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73013123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Laplace Transform of nested analytic functions via Bell’s polynomials 用贝尔多项式进行嵌套解析函数的拉普拉斯变换
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-31 DOI: 10.31197/atnaa.1187617
P. Ricci, D. Caratelli, S. Pinelas
{"title":"Laplace Transform of nested analytic functions via Bell’s polynomials","authors":"P. Ricci, D. Caratelli, S. Pinelas","doi":"10.31197/atnaa.1187617","DOIUrl":"https://doi.org/10.31197/atnaa.1187617","url":null,"abstract":"Bell's polynomials have been used in many different fields, ranging from number theory to operators theory. In this article we show a method to compute the Laplace Transform (LT) of nested analytic functions. To this aim, we provide a table of the first few values of the complete Bell's polynomials, which are then used to evaluate the LT of composite exponential functions. Furthermore a code for approximating the Laplace Transform of general analytic composite functions is created and presented. A graphical verification of the proposed technique is illustrated in the last section.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81741584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient spectral Legendre Galerkin approach for the advection diffusion equation with constant and variable coefficients under mixed Robin boundary conditions 混合Robin边界条件下常变系数平流扩散方程的高效谱Legendre Galerkin方法
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-31 DOI: 10.31197/atnaa.1139533
Zineb Laouar, N. Arar, Abdel-Fattah Talaat
{"title":"Efficient spectral Legendre Galerkin approach for the advection diffusion equation with constant and variable coefficients under mixed Robin boundary conditions","authors":"Zineb Laouar, N. Arar, Abdel-Fattah Talaat","doi":"10.31197/atnaa.1139533","DOIUrl":"https://doi.org/10.31197/atnaa.1139533","url":null,"abstract":"This paper aims to develop a numerical approximation for the solution of the advection-diffusion equation with constant and variable coefficients. We propose a numerical solution for the equation associated with Robin's mixed boundary conditions perturbed with a small parameter $varepsilon$. The approximation is based on a couple of methods: A spectral method of Galerkin type with a basis composed from Legendre-polynomials and a Gauss quadrature of type Gauss-Lobatto applied for integral calculations with a stability and convergence analysis. In addition, a Crank-Nicolson scheme is used for temporal solution as a finite difference method. Several numerical examples are discussed to show the efficiency of the proposed numerical method, specially when $varepsilon$ tends to zero so that we obtain the exact solution of the classic problem with homogeneous Dirichlet boundary conditions. The numerical convergence is well presented in different examples. Therefore, we build an efficient numerical method for different types of partial differential equations with different boundary conditions.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79597999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Sequential Differential Problem With Caputo and Riemann Liouville Derivatives Involving Convergent Series 包含收敛级数的Caputo和Riemann Liouville导数的序列微分问题
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-30 DOI: 10.31197/atnaa.1224234
Mahdi Rakah
{"title":"A Sequential Differential Problem With Caputo and Riemann Liouville Derivatives Involving Convergent Series","authors":"Mahdi Rakah","doi":"10.31197/atnaa.1224234","DOIUrl":"https://doi.org/10.31197/atnaa.1224234","url":null,"abstract":"In this paper, we study a new nonlinear sequential differential prob- \u0000lem with nonlocal integral conditions that involve convergent series. The \u0000problem involves two fractional order operators: Riemann-Liouville inte- \u0000gral, Caputo and Riemann-Liouville derivatives. We prove an existence \u0000and uniqueness result. Also, we prove a new existence result. We end our \u0000paper by presenting some illustrative examples.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79501380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New existence result under weak topology for fractional differential equations 分数阶微分方程弱拓扑下新的存在性结果
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-24 DOI: 10.31197/atnaa.1235476
Hallaci Ahmed, Professor DR., Krichen Bi̇lel, Mefteh Bi̇lel
{"title":"New existence result under weak topology for fractional differential equations","authors":"Hallaci Ahmed, Professor DR., Krichen Bi̇lel, Mefteh Bi̇lel","doi":"10.31197/atnaa.1235476","DOIUrl":"https://doi.org/10.31197/atnaa.1235476","url":null,"abstract":"This paper deals with the existence of weak solutions for an initial value problem involving Riemann-Liouville-type fractional derivatives. To this end, we transform the posed problem to a sum of two integral operators, then we apply a variant of Krasnoselskii’s fixed point theorem under weak topology to conclude the existence of weak solutions.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85127091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(G'/G)-EXPANSION METHOD TO SEEK TRAVELING WAVE SOLUTIONS FOR SOME FRACTIONAL NONLINEAR PDES ARISING IN NATURAL SCIENCES (g′/ g)展开法求解自然科学中某些分数阶非线性方程的行波解
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-22 DOI: 10.31197/atnaa.1125691
Medjahed Djilali, Hakem Ali
{"title":"(G'/G)-EXPANSION METHOD TO SEEK TRAVELING WAVE SOLUTIONS FOR SOME FRACTIONAL NONLINEAR PDES ARISING IN NATURAL SCIENCES","authors":"Medjahed Djilali, Hakem Ali","doi":"10.31197/atnaa.1125691","DOIUrl":"https://doi.org/10.31197/atnaa.1125691","url":null,"abstract":"The (G'/G)-expansion method with the aid of symbolic computational system can be used to obtain the traveling wave solutions (hyperbolic, trigonometric and rational solutions) for nonlinear time-fractional evolution equations arising in mathematical physics and biology. In this work, we will process the analytical solutions of the time-fractional classical Boussinesq equation, the time-fractional Murray equation, and the space-time fractional Phi-four equation. With the fact that the method which we will propose in this paper is also a standard, direct and computerized method, the exact solutions for these equations are obtained.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76296127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A new computational approach for solving a boundary-value problem for DEPCAG 求解DEPCAG边值问题的一种新的计算方法
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-11 DOI: 10.31197/atnaa.1202501
Zh. M. Kadirbayeva, A. Assanova, E. Bakirova
{"title":"A new computational approach for solving a boundary-value problem for DEPCAG","authors":"Zh. M. Kadirbayeva, A. Assanova, E. Bakirova","doi":"10.31197/atnaa.1202501","DOIUrl":"https://doi.org/10.31197/atnaa.1202501","url":null,"abstract":"In this paper, a new computational approach is presented to solve a boundary-value problem for a differential equation with piecewise constant argument of generalized type (DEPCAG). The presented technique is based on the Dzhumabaev parametrization method. A useful numerical algorithm is developed to obtain the numerical values from the problem. Numerical experiments are conducted to demonstrate the accuracy and efficiency.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77132820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An asymptotic homogenization formula for complex permittivity and its application 复介电常数的渐近均匀化公式及其应用
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-03-08 DOI: 10.31197/atnaa.1223064
V. Mityushev, T. Gric, Z. Zhunussova, K. Dosmagulova
{"title":"An asymptotic homogenization formula for complex permittivity and its application","authors":"V. Mityushev, T. Gric, Z. Zhunussova, K. Dosmagulova","doi":"10.31197/atnaa.1223064","DOIUrl":"https://doi.org/10.31197/atnaa.1223064","url":null,"abstract":"The $mathbb R$-linear boundary value problem in a multiply connected domain on a flat torus is considered. This problem is closely related to the Riemann-Hilbert problem on analytic functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of components. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains location of inclusions in symbolic form. The application of the derived formula to investigation of the morphology of the tumor cells in disordered biological media is discussed.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91334311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On boundary value problems for the Boussinesq-type equation with dynamic and non-dynamic boundary conditions 具有动态和非动态边界条件的boussinesq型方程的边值问题
Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2023-02-17 DOI: 10.31197/atnaa.1215178
M. Jenaliyev, A. Kassymbekova, M. Yergaliyev, Bekzat Orynbasar
{"title":"On boundary value problems for the Boussinesq-type equation with dynamic and non-dynamic boundary conditions","authors":"M. Jenaliyev, A. Kassymbekova, M. Yergaliyev, Bekzat Orynbasar","doi":"10.31197/atnaa.1215178","DOIUrl":"https://doi.org/10.31197/atnaa.1215178","url":null,"abstract":"The work studies boundary value problems with non-dynamic and dynamic boundary conditions for one- and two-dimensional Boussinesq-type equations in domains representing a trapezoid, triangle, \"curvilinear\" trapezoid, \"curvilinear\" triangle, truncated cone, cone, truncated \"curvilinear\" cone, and \"curvilinear\" cone. Combining the methods of the theory of monotone operators and a priori estimates, in Sobolev classes, we have established theorems on the unique weak solvability of the boundary value problems under study.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76070245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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