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International Journal of Differential Equations最新文献

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Solving First-Order Differential Equations of Z-Numbers’ Initial Value Using Radial Basic Function 用径向基函数求解Z数初值的一阶微分方程
IF 1.6
International Journal of Differential Equations Pub Date : 2020-05-26 DOI: 10.1155/2020/5924847
Leila Qalehe, M. Afshar Kermani, T. Allahviranloo
{"title":"Solving First-Order Differential Equations of Z-Numbers’ Initial Value Using Radial Basic Function","authors":"Leila Qalehe, M. Afshar Kermani, T. Allahviranloo","doi":"10.1155/2020/5924847","DOIUrl":"https://doi.org/10.1155/2020/5924847","url":null,"abstract":"In this paper, a method was proposed based on RBF for numerical solution of first-order differential equations with initial values that are valued by Z-numbers. The proposed method consists of two parts. The first part has stated the amount of limitation of the fragmentation solution, while the second part has described the assurance of the first part. The limitation section also has two parts. The first part has included the initial condition of the problem, while the second part has included the RBF network. The confidence interval was also considered as a function based on the probability function, which has calculated the confidence level of the first part (limitation). The RBF network or the radial-base grid network has three distinct layers: the input layer that is the set of elementary nodes (sensory units); the second layer is the hidden layers with high dimensions, in which the output layer that has responded to the network response and the activation patterns used in the input layer. The advantage of using RBF is that the use of this technique does not require sufficient information. It only relies on the domain and the boundary. In an example, we have showed that our proposed approach could approximate the problem with acceptable confidence.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/5924847","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47896866","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
Second-Order Elliptic Equation with Singularities 二阶奇异椭圆方程
IF 1.6
International Journal of Differential Equations Pub Date : 2020-05-20 DOI: 10.1155/2020/4589864
Hichem Boughazi
{"title":"Second-Order Elliptic Equation with Singularities","authors":"Hichem Boughazi","doi":"10.1155/2020/4589864","DOIUrl":"https://doi.org/10.1155/2020/4589864","url":null,"abstract":"On the compact Riemannian manifold of dimension , we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-16"},"PeriodicalIF":1.6,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4589864","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47749484","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
Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients 具时变系数的保形时空分数阶Zeldovich方程的精确解
IF 1.6
International Journal of Differential Equations Pub Date : 2020-05-12 DOI: 10.1155/2020/9312830
S. Injrou
{"title":"Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients","authors":"S. Injrou","doi":"10.1155/2020/9312830","DOIUrl":"https://doi.org/10.1155/2020/9312830","url":null,"abstract":"The aim of this paper is to improve a sub-equation method to solve the space-time fractional Zeldovich equation with time-dependent coefficients involving the conformable fractional derivative. As result, we obtain three families of solutions including the hyperbolic, trigonometric, and rational solutions. These solutions may be helpful to explain several phenomena in chemistry, including the combustion process. The study shows that the used method is effective and reliable and can be utilized as a substitution to construct new solutions of different types of nonlinear conformable fractional partial differential equations (NFPDEs) with variable coefficients.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-6"},"PeriodicalIF":1.6,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/9312830","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49124889","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: 5
Multiple Solutions for Ellipticpx,qx-Kirchhoff-Type Potential Systems in Unbounded Domains 无界域上Ellipticpx,qx- kirchhoff型势系统的多重解
IF 1.6
International Journal of Differential Equations Pub Date : 2020-04-24 DOI: 10.1155/2020/3438169
Nabil Chems Eddine, A. El Hachimi
{"title":"Multiple Solutions for Ellipticpx,qx-Kirchhoff-Type Potential Systems in Unbounded Domains","authors":"Nabil Chems Eddine, A. El Hachimi","doi":"10.1155/2020/3438169","DOIUrl":"https://doi.org/10.1155/2020/3438169","url":null,"abstract":"In this paper, we establish the existence of at least three weak solutions for a parametric double eigenvalue quasi-linear elliptic - Kirchhoff-type potential system. Our approach is based on a variational method, and a three critical point theorem is obtained by Bonano and Marano.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-9"},"PeriodicalIF":1.6,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/3438169","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46291018","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: 1
An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model 二维时空SEIR流行病模型的最优控制
IF 1.6
International Journal of Differential Equations Pub Date : 2020-04-04 DOI: 10.1155/2020/4749365
K. Adnaoui, Adil El Alami Laaroussi
{"title":"An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model","authors":"K. Adnaoui, Adil El Alami Laaroussi","doi":"10.1155/2020/4749365","DOIUrl":"https://doi.org/10.1155/2020/4749365","url":null,"abstract":"In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-15"},"PeriodicalIF":1.6,"publicationDate":"2020-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4749365","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47634209","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: 10
Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods 同意-不同意模型的稳定性和全局灵敏度分析：偏秩相关系数和拉丁超立方体抽样方法
IF 1.6
International Journal of Differential Equations Pub Date : 2020-04-01 DOI: 10.1155/2020/5051248
S. Bidah, O. Zakary, M. Rachik
{"title":"Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods","authors":"S. Bidah, O. Zakary, M. Rachik","doi":"10.1155/2020/5051248","DOIUrl":"https://doi.org/10.1155/2020/5051248","url":null,"abstract":"In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-14"},"PeriodicalIF":1.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/5051248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44945129","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: 20
An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag 求解时滞捕食-食饵模型的改进欧拉多项式与伯努利多项式的搭配方法
IF 1.6
International Journal of Differential Equations Pub Date : 2020-04-01 DOI: 10.1155/2020/9176784
B. Basirat, H. Elahi
{"title":"An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag","authors":"B. Basirat, H. Elahi","doi":"10.1155/2020/9176784","DOIUrl":"https://doi.org/10.1155/2020/9176784","url":null,"abstract":"This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/9176784","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42724392","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: 2
Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order 一类分数阶耦合混合微分方程组的存在性结果
IF 1.6
International Journal of Differential Equations Pub Date : 2020-03-20 DOI: 10.1155/2020/3038427
M. Hannabou, K. Hilal
{"title":"Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order","authors":"M. Hannabou, K. Hilal","doi":"10.1155/2020/3038427","DOIUrl":"https://doi.org/10.1155/2020/3038427","url":null,"abstract":"This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-8"},"PeriodicalIF":1.6,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/3038427","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48855363","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: 2
An Investigation of Solving Third-Order Nonlinear Ordinary Differential Equation in Complex Domain by Generalising Prelle–Singer Method 用广义prele - singer方法求解复域三阶非线性常微分方程的研究
IF 1.6
International Journal of Differential Equations Pub Date : 2020-03-17 DOI: 10.1155/2020/5276024
Ali K. Joohy, Ghassan A. Al-Juaifri, M. Mechee
{"title":"An Investigation of Solving Third-Order Nonlinear Ordinary Differential Equation in Complex Domain by Generalising Prelle–Singer Method","authors":"Ali K. Joohy, Ghassan A. Al-Juaifri, M. Mechee","doi":"10.1155/2020/5276024","DOIUrl":"https://doi.org/10.1155/2020/5276024","url":null,"abstract":"A method to solve a family of third-order nonlinear ordinary complex differential equations (NLOCDEs) —nonlinear ODEs in the complex plane—by generalizing Prelle–Singer has been developed. The approach that the authors generalized is a procedure of obtaining a solution to a kind of second-order nonlinear ODEs in the real line. Some theoretical work has been illustrated and applied to several examples. Also, an extended technique of generating second and third motion integrals in the complex domain has been introduced, which is conceptually an analog to the motion in the real line. Moreover, the procedures of the method mentioned above have been verified.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/5276024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46873147","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
Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition 具有积分边界条件的奇摄动问题的加速指数拟合算子方法
IF 1.6
International Journal of Differential Equations Pub Date : 2020-03-16 DOI: 10.1155/2020/9268181
H. Debela, G. Duressa
{"title":"Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition","authors":"H. Debela, G. Duressa","doi":"10.1155/2020/9268181","DOIUrl":"https://doi.org/10.1155/2020/9268181","url":null,"abstract":"In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be - uniformly convergent.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-8"},"PeriodicalIF":1.6,"publicationDate":"2020-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/9268181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46055009","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: 5
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