{"title":"Periodic solution for neutral-type differential equation with piecewise impulses on time scales","authors":"Chun Peng, Xiaoliang Li, Bo Du","doi":"10.1186/s13661-024-01916-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01916-5","url":null,"abstract":"In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the existence of a unique periodic solution by using the Banach contraction mapping principle. We also prove the existence of at least one periodic solution using the Schauder fixed point theorem. In addition, we establish the stability results based on the existence of periodic solutions. It is worth noting that the results of this paper are based on time scales, so that they are applicable to continuous, discrete, and other types of systems.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197440","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}
{"title":"The multiple birth properties of multi-type Markov branching processes","authors":"Junping Li, Wanting Zhang","doi":"10.1186/s13661-024-01914-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01914-7","url":null,"abstract":"The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197438","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}
{"title":"Boundedness of solutions to a second-order periodic system with p-Laplacian and unbounded perturbation terms","authors":"Xiumei Xing, Haiyan Wang, Shaoyong Lai","doi":"10.1186/s13661-024-01911-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01911-w","url":null,"abstract":"The second-order periodic system with p-Laplacian and unbounded time-dependent perturbation terms is investigated. Using the principle integral method, it is shown that under certain assumptions on the unbounded and periodic terms, all solutions to the equation possess boundedness.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"27 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197315","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}
{"title":"Adopted spectral tau approach for the time-fractional diffusion equation via seventh-kind Chebyshev polynomials","authors":"W. M. Abd-Elhameed, Y. H. Youssri, A. G. Atta","doi":"10.1186/s13661-024-01907-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01907-6","url":null,"abstract":"This study utilizes a spectral tau method to acquire an accurate numerical solution of the time-fractional diffusion equation. The central point of this approach is to use double basis functions in terms of certain Chebyshev polynomials, namely Chebyshev polynomials of the seventh-kind and their shifted ones. Some new formulas concerned with these polynomials are derived in this study. A rigorous error analysis of the proposed double expansion further corroborates our research. This analysis is based on establishing some inequalities regarding the selected basis functions. Several numerical examples validate the precision and effectiveness of the suggested method.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225221","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}
{"title":"New results on fractional advection–dispersion equations","authors":"Yan Qiao, Fangqi Chen, Yukun An, Tao Lu","doi":"10.1186/s13661-024-01910-x","DOIUrl":"https://doi.org/10.1186/s13661-024-01910-x","url":null,"abstract":"In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Caputo fractional derivatives. Since the nonlinear terms contain fractional derivatives, this problem does not directly have variational structure, we need to combine critical point theory and an iterative method to deal with such problems. Finally, the existence of at least one nontrivial solution is proved by the mountain pass theorem and the iterative method. At the same time, an example is given to illustrate the main result.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"68 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197441","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}
Abdelghani Lakhdari, Hüseyin Budak, Muhammad Uzair Awan, Badreddine Meftah
{"title":"Extension of Milne-type inequalities to Katugampola fractional integrals","authors":"Abdelghani Lakhdari, Hüseyin Budak, Muhammad Uzair Awan, Badreddine Meftah","doi":"10.1186/s13661-024-01909-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01909-4","url":null,"abstract":"This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"32 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197442","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}
{"title":"Nondegeneracy of the solutions for elliptic problem with critical exponent","authors":"Qingfang Wang","doi":"10.1186/s13661-024-01908-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01908-5","url":null,"abstract":"This paper deals with the following nonlinear elliptic equation: $$ -Delta u=Q(|y'|,y'')u^{frac{N+2}{N-2}},,,u>0,,,text{in},{ mathbb{R}}^{N},,,uin D^{1,2}({mathbb{R}}^{N}), $$ where $(y',y'')in {mathbb{R}}^{2}times {mathbb{R}}^{N-2}$ , $Ngeq 5$ , $Q(|y'|,y'')$ is a bounded nonnegative function in $mathbb{R}^{2}times {mathbb{R}}^{N-2}$ . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019).","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"105 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933522","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}
{"title":"Bifurcation curve for the Minkowski-curvature equation with concave or geometrically concave nonlinearity","authors":"Kuo-Chih Hung","doi":"10.1186/s13661-024-01906-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01906-7","url":null,"abstract":"We study the bifurcation curve and exact multiplicity of positive solutions in the space $C^{2}left ( (-L,L)right ) cap Cleft ( [-L,L]right ) $ for the Minkowski-curvature equation $$ left { textstylebegin{array}{l} -left ( dfrac{u^{prime }(x)}{sqrt{1-left ( {u^{prime }(x)}right ) ^{2}}}right ) ^{prime }=lambda f(u),text{ }-L< x< L, u(-L)=u(L)=0.end{array}displaystyle right . $$ where $lambda >0$ is a bifurcation parameter, $fin C[0,infty )cap C^{2}(0,infty )$ satisfies $f(u)>0$ for $u>0$ and f is either concave or geometrically concave on $(0,infty )$ . If f is a concave function, we prove that the bifurcation curve is monotone increasing on the $(lambda ,left Vert uright Vert _{infty })$ -plane. If f is a geometrically concave function, we prove that the bifurcation curve is either ⊂-shaped or monotone increasing on the $(lambda ,left Vert uright Vert _{infty })$ -plane under a mild condition. Some interesting applications are given.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"39 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933523","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}
{"title":"Existence of positive solutions for a class of p-Laplacian fractional differential equations with nonlocal boundary conditions","authors":"Jiqiang Jiang, Xuelin Sun","doi":"10.1186/s13661-024-01905-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01905-8","url":null,"abstract":"This article is devoted to proving the uniqueness of positive solutions for p-Laplacian equations with Caputo and Riemann-Liouville fractional derivative. The uniqueness result and the dependence of the solution on a parameter are established based on the fixed point point theorem of mixed monotone operators. In the end, a numerical simulation is given to verify the main results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933524","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}
Suleman Alfalqi, Boumediene Boukhari, Ahmed Bchatnia, Abderrahmane Beniani
{"title":"Advanced neural network approaches for coupled equations with fractional derivatives","authors":"Suleman Alfalqi, Boumediene Boukhari, Ahmed Bchatnia, Abderrahmane Beniani","doi":"10.1186/s13661-024-01899-3","DOIUrl":"https://doi.org/10.1186/s13661-024-01899-3","url":null,"abstract":"We investigate numerical solutions and compare them with Fractional Physics-Informed Neural Network (FPINN) solutions for a coupled wave equation involving fractional partial derivatives. The problem explores the evolution of functions u and v over time t and space x. We employ two numerical approximation schemes based on the finite element method to discretize the system of equations. The effectiveness of these schemes is validated by comparing numerical results with exact solutions. Additionally, we introduce the FPINN method to tackle the coupled equation with fractional derivative orders and compare its performance against traditional numerical methods. Key findings reveal that both numerical approaches provide accurate solutions, with the FPINN method demonstrating competitive performance in terms of accuracy and computational efficiency. Our study highlights the significance of employing FPINNs in solving fractional differential equations and underscores their potential as alternatives to conventional numerical methods. The novelty of this work lies in its comparative analysis of traditional numerical techniques and FPINNs for solving coupled wave equations with fractional derivatives, offering insights into advancing computational methods for complex physical systems.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"188 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884359","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}