Journal of Integral Equations and Applications最新文献

{"title":"Weighted Cauchy problem: fractional versus integer order","authors":"M. G. Morales, Z. Došlá","doi":"10.1216/jie.2021.33.497","DOIUrl":"https://doi.org/10.1216/jie.2021.33.497","url":null,"abstract":"This work is devoted to the solvability of the weighted Cauchy problem for fractional differential equations of arbitrary order, considering the Riemann-Liouville derivative. We show the equivalence between the weighted Cauchy problem and the Volterra integral equation in the space of Lebesgue integrable functions. Finally, we point out some discrepancies between the solutions for fractional and integer order case.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48533150","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":"Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP in 2D with general right-hand side","authors":"T. Ayele, S. Mikhailov","doi":"10.1216/jie.2021.33.403","DOIUrl":"https://doi.org/10.1216/jie.2021.33.403","url":null,"abstract":"Applying the two-operator approach, the mixed (Dirichlet-Neumann) boundary value problem for a second-order scalar elliptic differential equation with variable coefficient is reduced to several systems of Boundary Domain Integral Equations, briefly BDIEs. The two-operator BDIE sys- tem equivalence to the boundary value problem, BDIE solvability and invertibility of the boundary- domain integral operators are proved in the appropriate Sobolev spaces.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42873150","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":"Carleman estimates and unique continuation property for N-dimensional Benjamin–Bona–Mahony equations","authors":"A. Esfahani, Y. Mammeri","doi":"10.1216/jie.2021.33.443","DOIUrl":"https://doi.org/10.1216/jie.2021.33.443","url":null,"abstract":"We study the unique continuation property for the N -dimensional BBM equations using Carleman estimates. We prove that if the solution of this equation vanishes in an open subset, then this solution is identically equal to zero in the horizontal component of the open subset.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47646849","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":"Uniqueness of the partial integro-differential equations","authors":"Chenkuan Li","doi":"10.1216/jie.2021.33.463","DOIUrl":"https://doi.org/10.1216/jie.2021.33.463","url":null,"abstract":"Summary: We study the uniqueness of solutions for certain partial integro-differential equations with the initial conditions in a Banach space. The results derived are new and based on Babenko’s approach, convolution and Banach’s contraction principle. We also include several examples for the illustration of main theorems.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" 54","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41252166","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":"Stable and convergent difference schemes for weakly singular convolution integrals","authors":"W. Davis, R. Noren","doi":"10.1216/jie.2021.33.271","DOIUrl":"https://doi.org/10.1216/jie.2021.33.271","url":null,"abstract":"We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order integrals using Taylor and fractional Taylor series expansions and grouping terms in a novel manner. A fractional Taylor series expansion argument is utilized to provide fractional-order approximations for functions with minimal regularity. The resulting schemes allow for the approximation of functions in C [0, T ], where 0 < γ ≤ 5. A mild invertibility criterion is provided for the implicit schemes. Consistency and stability are proven separately for the whole-number-order approximations and the fractional-order approximations. The rate of convergence in the time variable is shown to be O(τ), 0 < γ ≤ 5 for u ∈ C [0, T ], where τ is the size of the partition of the time mesh. Crucially, the assumption of the integral kernel K being decreasing is not required for the scheme to converge in second-order and below approximations. Optimal convergence results are then proven for both sets of approximations, where fractional-order approximations can obtain up to whole-number rate of convergence in certain scenarios. Finally, numerical examples are provided that illustrate our findings. 2000 Mathematics Subject Classification. 26A33, 45D05, 65R20.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49243223","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":"Asymptotic behavior of solutions of Volterra integro-differential equations with and without retardation","authors":"J. Graef, O. Tunç","doi":"10.1216/jie.2021.33.289","DOIUrl":"https://doi.org/10.1216/jie.2021.33.289","url":null,"abstract":"Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro-differential equations with and without constant retardation are investigated using a new type of Lyapunov-Krasovskii functionals. An advantage of the new functionals used here is that they eliminate using Gronwall’s inequality. Compared to related results in the literature, the conditions here are more general, simple, and convenient to apply. Examples to show the application of the theorems are included.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43577718","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":"Global solvability for nonlinear nonautonomous evolution inclusions of Volterra-type and its applications","authors":"Yanghai Yu, Zhongjie Ma","doi":"10.1216/jie.2021.33.381","DOIUrl":"https://doi.org/10.1216/jie.2021.33.381","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"193 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41277062","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":"Multiplicity of nontrivial solutions for a class of fractional elliptic equations","authors":"T. Kenzizi","doi":"10.1216/jie.2021.33.315","DOIUrl":"https://doi.org/10.1216/jie.2021.33.315","url":null,"abstract":"In this paper, we are concerned with the following fractional Laplacian equation (−∆)u = a(x)|u(x)|q−2u(x) + λb(x)|u(x)|p−2u(x) in (−1, 1), u > 0 in (−1, 1), u = 0 in R (−1, 1), where s ∈ (0, 1), λ > 0. Using variational methods, we show existence and multiplicity of positive solutions.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47371061","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 weak solutions for a new class of fractional boundary value impulsive systems with Riemann–Liouville derivatives","authors":"R. Guefaifia, S. Boulaaras, Fares Kamache","doi":"10.1216/jie.2021.33.301","DOIUrl":"https://doi.org/10.1216/jie.2021.33.301","url":null,"abstract":"The existence of three solutions for perturbed systems of impulsive non-linear fractional di¤erential equations together with Lipschitz continuous non-linear terms is discussed in this paper. The idea relies on variational methods. Moreover, an example is presented in order to summarize the feasibility and e¤ectiveness of the main results. 1. Introduction In this work, we aim to study the perturbed impulsive fractional di¤erential system: (1.1) 8&gt;&lt;&gt;&gt;&gt;&gt;: tD i T (ai (t) 0D i t ui (t)) = Fui (t; u) + Gui (t; u) + hi (ui (t)) ; t 2 [0; T ] ; t 6= tj 4 tD i 1 T ( c 0D i t ui) (tj) = Iij (ui (tj)) ; j = 1; 2; ;m ui (0) = ui (T ) = 0 ; for 1 i n; where u = (u1; u2; ; un) ; n 2; 0 &lt; i 1 for 1 i n; &gt; 0; &gt; 0; T &gt; 0; ai 2 L1 ([0; T ]) ; ai = ess inf t2[0;T ] ai (t) &gt; 0 i.e kaik1 = inf C 2 R; jaij C ; 0D i t and tD i T designate the left and right Riemann–Liouville fractional derivatives of order i respectively, F;G : [0; T ] R ! R are quanti\u0085able with respect to t, for all u 2 R; continuously di¤erentiable in u, for approximately every t 2 [0; T ] such that F1) For every &gt; 0 and every 1 i n, n supj j & jF ( ; )j ; supj j & jG ( ; )j o 2 L ([0; T ]) ; for any &gt; 0 with = ( 1; 2; ; n) and j j = qPn i=1 2 i : F2) F (t; 0; ; 0) = 0; for every t 2 [0; T ] : hi : R ! R is a Lipschitz continuous function with the Lipschitz constant Li &gt; 0; i:e: Date : October 10th, 2020. 1991 Mathematics Subject Classi\u0085cation. 35J60, 35B30, 35B40. Key words and phrases. AMS subject classi\u0085cations: (2000) 35J60 35B30 35B40. *Corresponding author. 1 10 Oct 2020 10:16:52 PDT 200120-Boulaaras Version 4 Submitted to J. Integr. Eq. Appl. 2 FARES KAMACHE, SALAH BOULAARAS ,3 ; RAFIK GUEFAIFIA jhi ( 1) hi ( 2)j Li j 1 2j for every 1; 2 2 R; satisfying hi (0) = 0 for 1 i n; Iij 2 C (R;R) for i = 1; ; n; j = 1; ;m; 0 = t0 &lt; t1 &lt; t2 &lt; &lt; tm &lt; tm+1 = T: The operator is de\u0085ned as 4 tD i 1 T ( c 0D i t ui) (tj) =t D i 1 T ( c 0D i t ui) t+j t D i 1 T ( c 0D i t ui) t j where tD i 1 T ( c 0D i t ui) t+j = lim t!t+j tD i 1 T ( c 0D i t ui) (t) and tD i 1 T ( c 0D i t ui) t j = lim t!t j tD i 1 T ( c 0D i t ui) (t) and 0D i T represents the left Caputo fractional derivatives with an i order. While, Fui and Gui respectively represent the partial derivatives of F and G following ui for 1 i n: Recently, Fractional Di¤erential Equations (FDEs) have emerged as important approaches that can be used to describe numerous phenomena in several \u0085elds of science such as physics and engineering. In fact, many applications related to viscoelasticity and porous media, as well as electrochemistry and electromagnetic can be modeled through the FDEs (see [15], [27], [33], [32] and [41] ). In the last few years, many papers focused on the search of solutions to boundary value problems for FDEs, we may refer to ([42], [4], [5], [13], [16], [18], [20], [21], [28], [34], [37], [38], [39] and [40]) and the references therein. It is worthy of note that Zhang et al. [46] have checked the existence of di¤erent solutions for a","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44185502","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 and continuity results for a nonlinear fractional Langevin equation with a weakly singular source","authors":"Nguyen Minh Dien","doi":"10.1216/jie.2021.33.349","DOIUrl":"https://doi.org/10.1216/jie.2021.33.349","url":null,"abstract":"We study a nonlinear Langevin equation involving a Caputo fractional derivatives of a function with respect to another function in a Banach space. Unlike previous papers, we assume the source function having a singularity. Under a regularity assumption of solution of the problem, we show that the problem can be transformed to a Volterra integral equation with two parameters Mittag-Leffler function in the kernel. Base on the obtained Volterra integral equation, we investigate the existence and uniqueness of the mild solution of the problem. Moreover, we show that the mild solution of the problem is dependent continuously on the inputs: initial data, fractional orders, appropriate function, and friction constant. Meanwhile, a new Henry-Gronwall type inequality is established to prove the main results of the paper. Examples illustrating our results are also presented.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41521159","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}