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Foundations of generalized Prabhakar-Hilfer fractional calculus with applications 广义Prabhakar-Hilfer分式微积分的基础及其应用
IF 0.5
Cubo Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300423
G. Anastassiou
{"title":"Foundations of generalized Prabhakar-Hilfer fractional calculus with applications","authors":"G. Anastassiou","doi":"10.4067/s0719-06462021000300423","DOIUrl":"https://doi.org/10.4067/s0719-06462021000300423","url":null,"abstract":"Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper bounds for them. We present several left and right side generalized Prabhakar fractional inequalities of Hardy, Opial and Hilbert-Pachpatte types. We apply these in the setting of generalized Hilfer calculus.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43472704","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
Extension of Exton’s hypergeometric function K16 Exton超几何函数K16的推广
IF 0.5
Cubo Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300489
Ahmed Ali Atash, Maisoon Ahmed Kulib
{"title":"Extension of Exton’s hypergeometric function K16","authors":"Ahmed Ali Atash, Maisoon Ahmed Kulib","doi":"10.4067/s0719-06462021000300489","DOIUrl":"https://doi.org/10.4067/s0719-06462021000300489","url":null,"abstract":"The purpose of this article is to introduce an extension of Exton’s hypergeometric function K 16 by using the extended beta function given by Özergin et al. [11]. Some integral representations, generating functions, recurrence relations, transformation formulas, derivative formula and summation formulas are obtained for this extended function. Some special cases of the main results of this paper are also considered.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44502435","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 the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators 用半Fredholm算子研究一类时滞偏微分方程的周期解
IF 0.5
Cubo Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300469
A. Elazzouzi, K. Ezzinbi, Mohammed Kriche
{"title":"On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators","authors":"A. Elazzouzi, K. Ezzinbi, Mohammed Kriche","doi":"10.4067/s0719-06462021000300469","DOIUrl":"https://doi.org/10.4067/s0719-06462021000300469","url":null,"abstract":"The main goal of this work is to examine the periodic dynamic behavior of some retarded periodic partial differential equations (PDE). Taking into consideration that the linear part realizes the Hille-Yosida condition, we discuss the Massera’s problem to this class of equations. Especially, we use the perturbation theory of semi-Fredholm operators and the Chow and Hale’s fixed point theorem to study the relation between the boundedness and the periodicity of solutions for some inhomogeneous linear retarded PDE. An example is also given at the end of this work to show the applicability of our theoretical results.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47746567","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
Basic asymptotic estimates for powers of Wallis’ ratios Wallis比率幂的基本渐近估计
IF 0.5
Cubo Pub Date : 2021-12-01 DOI: 10.4067/s0719-06462021000300357
V. Lampret
{"title":"Basic asymptotic estimates for powers of Wallis’ ratios","authors":"V. Lampret","doi":"10.4067/s0719-06462021000300357","DOIUrl":"https://doi.org/10.4067/s0719-06462021000300357","url":null,"abstract":"For any a ∈ R , for every n ∈ N , and for n -th Wallis’ ratio w n := (cid:81) nk =1 2 k − 1 2 k , the relative error r 0 ( a, n ) := (cid:0) v 0 ( a, n ) − w an (cid:1) /w an of the approximation w an ≈ v 0 ( a, n ) := ( πn ) − a/ 2 is estimated as (cid:12)(cid:12) r 0 ( a, n ) (cid:12)(cid:12) < 14 n . The improvement w an ≈ v ( a, n ) := ( πn ) − a/ 2 (cid:16) 1 − a 8 n + a 2 128 n 2 (cid:17) is also studied.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42125308","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
Dirichlet series and series with Stirling numbers 狄利克雷级数和斯特林级数
IF 0.5
Cubo Pub Date : 2021-09-19 DOI: 10.56754/0719-0646.2501.103
K. Boyadzhiev
{"title":"Dirichlet series and series with Stirling numbers","authors":"K. Boyadzhiev","doi":"10.56754/0719-0646.2501.103","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.103","url":null,"abstract":"This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers, binomial coefficients, central binomial coefficients, and Catalan numbers.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48248589","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 new class of graceful graphs: k-enriched fan graphs and their characterisations 一类新的优美图：k-富集扇形图及其特征
IF 0.5
Cubo Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200313
M. Haviar, S. Kurtulík
{"title":"A new class of graceful graphs: k-enriched fan graphs and their characterisations","authors":"M. Haviar, S. Kurtulík","doi":"10.4067/s0719-06462021000200313","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200313","url":null,"abstract":"The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years. \u0000Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of (k)-enriched fan graphs (kF_n) for all integers (k, nge 2) and we prove that these graphs are graceful. Moreover, we provide characterizations of the (k)-enriched fan graphs (kF_n) among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41618345","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 Rellich's Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces 复空间上算子的Rellich引理、poincar<s:1>不等式和Friedrichs推广
IF 0.5
Cubo Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200265
C. Tung, P. D. Lamberti
{"title":"On Rellich's Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces","authors":"C. Tung, P. D. Lamberti","doi":"10.4067/s0719-06462021000200265","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200265","url":null,"abstract":"This paper is mainly concerned with: (i) a generalization of the Rellich’s Lemma to a Riemann subdomain of a complex space, (ii) the Poincare inequality, and (iii) Friedrichs extension of a Schrodinger type operator. Applications to the eigenfunction expansion problem associated to the modified Laplacian are also given.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43373919","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
Approximate solution of Abel integral equation in Daubechies wavelet basis Daubechies小波基中Abel积分方程的近似解
IF 0.5
Cubo Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200245
Jyotirmoy Mouley, M. M. Panja, B. N. Mandal
{"title":"Approximate solution of Abel integral equation in Daubechies wavelet basis","authors":"Jyotirmoy Mouley, M. M. Panja, B. N. Mandal","doi":"10.4067/s0719-06462021000200245","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200245","url":null,"abstract":"This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48676007","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
Weakly strongly star-Menger spaces 弱强星门格尔空间
IF 0.5
Cubo Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200287
G. Kumar, B. Tyagi
{"title":"Weakly strongly star-Menger spaces","authors":"G. Kumar, B. Tyagi","doi":"10.4067/s0719-06462021000200287","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200287","url":null,"abstract":"A space (X) is called weakly strongly star-Menger space if for each sequence ((mathcal{U}_{n} : n in omega)) of open covers of (X), there is a sequence ((F_n : ninomega)) of finite subsets of (X) such that (overline{bigcup_{ninomega} St(F_n, mathcal{U}_n)}) is (X). In this paper, we investigate the relationship of weakly strongly star-Menger spaces with other related spaces. It is shown that a Hausdorff paracompact weakly star Menger (P)-space is star-Menger. We also study the images and preimages of weakly strongly star-Menger spaces under various type of maps.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48621965","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
Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces 部分有序度量空间中非线性压缩映射的重合点结果
IF 0.5
Cubo Pub Date : 2021-08-01 DOI: 10.4067/s0719-06462021000200207
K. Kalyani, N. S. Rao
{"title":"Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces","authors":"K. Kalyani, N. S. Rao","doi":"10.4067/s0719-06462021000200207","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200207","url":null,"abstract":"In this paper, we proved some coincidence point results for (f)- nondecreasing self-mapping satisfying certain rational type contractions in the context of a metric space endowed with a partial order. Moreover, some consequences of the main result are given by involving integral type contractions in the space. Some numerical examples are illustrated to support our results. As an application, we have discussed the existence of a unique solution of integral equation.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41717646","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
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