Lyes Ikhlef, Sedda Hakmi, Ouiza Lekadir, D. Aïssani
Abstract In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time, ( s , S ) left(s,S) replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system.
{"title":"Petri net analysis of a queueing inventory system with orbital search by the server","authors":"Lyes Ikhlef, Sedda Hakmi, Ouiza Lekadir, D. Aïssani","doi":"10.1515/dema-2022-0207","DOIUrl":"https://doi.org/10.1515/dema-2022-0207","url":null,"abstract":"Abstract In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time, ( s , S ) left(s,S) replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42186122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anupam Das, Marija Paunović, Vahid Parvaneh, M. Mursaleen, Z. Bagheri
Abstract In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.
{"title":"Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness","authors":"Anupam Das, Marija Paunović, Vahid Parvaneh, M. Mursaleen, Z. Bagheri","doi":"10.1515/dema-2022-0192","DOIUrl":"https://doi.org/10.1515/dema-2022-0192","url":null,"abstract":"Abstract In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48479805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduced a new general class of Prešić-type operators, by enriching the known class of Prešić contractions. We established conditions under which enriched Prešić operators possess a unique fixed point, proving the convergence of two different iterative methods to the fixed point. We also gave a data dependence result that was finally applied in proving the global asymptotic stability of the equilibrium of a certain k-th order difference equation.
{"title":"Asymptotic stability of equilibria for difference equations via fixed points of enriched Prešić operators","authors":"M. Pacurar","doi":"10.1515/dema-2022-0185","DOIUrl":"https://doi.org/10.1515/dema-2022-0185","url":null,"abstract":"Abstract We introduced a new general class of Prešić-type operators, by enriching the known class of Prešić contractions. We established conditions under which enriched Prešić operators possess a unique fixed point, proving the convergence of two different iterative methods to the fixed point. We also gave a data dependence result that was finally applied in proving the global asymptotic stability of the equilibrium of a certain k-th order difference equation.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42992990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary function involving the exponential function, the authors find increasing property and logarithmic convexity of two functions containing the gamma function and the Dirichlet lambda function.
{"title":"Increasing property and logarithmic convexity of functions involving Dirichlet lambda function","authors":"Feng Qi (祁锋), D. Lim","doi":"10.1515/dema-2022-0243","DOIUrl":"https://doi.org/10.1515/dema-2022-0243","url":null,"abstract":"Abstract In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary function involving the exponential function, the authors find increasing property and logarithmic convexity of two functions containing the gamma function and the Dirichlet lambda function.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48986893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations. Our theorems exhibit the forms of finite order transcendental entire solutions for these systems, which are some extensions and improvement of the previous theorems given by Xu, Cao, Liu, etc. Furthermore, we give a series of examples to show that the existence conditions and the forms of transcendental entire solutions with finite order of such systems are precise.
{"title":"The study of solutions for several systems of PDDEs with two complex variables","authors":"Yi-Hui Xu, Xiao Lan Liu, H. Xu","doi":"10.1515/dema-2022-0241","DOIUrl":"https://doi.org/10.1515/dema-2022-0241","url":null,"abstract":"Abstract The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations. Our theorems exhibit the forms of finite order transcendental entire solutions for these systems, which are some extensions and improvement of the previous theorems given by Xu, Cao, Liu, etc. Furthermore, we give a series of examples to show that the existence conditions and the forms of transcendental entire solutions with finite order of such systems are precise.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43594261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we are interested to study the elliptic equation under the Caputo derivative. We obtain several regularity results for the mild solution based on various assumptions of the input data. In addition, we derive the lower bound of the mild solution in the appropriate space. The main tool of the analysis estimation for the mild solution is based on the bound of the Mittag-Leffler functions, combined with analysis in Hilbert scales space. Moreover, we provide a regularized solution for our problem using the Fourier truncation method. We also obtain the error estimate between the regularized solution and the mild solution. Our current article seems to be the first study to deal with elliptic equations with Caputo derivatives on the unbounded domain.
{"title":"On initial value problem for elliptic equation on the plane under Caputo derivative","authors":"Tran Thanh Binh, Bui Dinh Thang, Nguyen Duc Phuong","doi":"10.1515/dema-2022-0257","DOIUrl":"https://doi.org/10.1515/dema-2022-0257","url":null,"abstract":"Abstract In this article, we are interested to study the elliptic equation under the Caputo derivative. We obtain several regularity results for the mild solution based on various assumptions of the input data. In addition, we derive the lower bound of the mild solution in the appropriate space. The main tool of the analysis estimation for the mild solution is based on the bound of the Mittag-Leffler functions, combined with analysis in Hilbert scales space. Moreover, we provide a regularized solution for our problem using the Fourier truncation method. We also obtain the error estimate between the regularized solution and the mild solution. Our current article seems to be the first study to deal with elliptic equations with Caputo derivatives on the unbounded domain.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.
{"title":"Properties of a subclass of analytic functions defined by Riemann-Liouville fractional integral applied to convolution product of multiplier transformation and Ruscheweyh derivative","authors":"A. Alb Lupaș, M. Acu","doi":"10.1515/dema-2022-0249","DOIUrl":"https://doi.org/10.1515/dema-2022-0249","url":null,"abstract":"Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohamed Hariri, Zohra Bouteffal, N. Beghersa, M. Benabdallah
Abstract In this article, we explain how a recent Lyapunov theorem on stability plays a role in the study of the strong stabilizability problem in Hilbert spaces. We explore a degenerate controlled system and investigate the properties of a feedback control to stabilize such system in depth. The spectral theory of an appropriate pencil operator is used to generate robustness constraints for a stabilizing control.
{"title":"On the stability of a strongly stabilizing control for degenerate systems in Hilbert spaces","authors":"Mohamed Hariri, Zohra Bouteffal, N. Beghersa, M. Benabdallah","doi":"10.1515/dema-2022-0238","DOIUrl":"https://doi.org/10.1515/dema-2022-0238","url":null,"abstract":"Abstract In this article, we explain how a recent Lyapunov theorem on stability plays a role in the study of the strong stabilizability problem in Hilbert spaces. We explore a degenerate controlled system and investigate the properties of a feedback control to stabilize such system in depth. The spectral theory of an appropriate pencil operator is used to generate robustness constraints for a stabilizing control.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45401741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, the behavior of hidden bifurcation in a two-dimensional (2D) scroll via saturated function series controlled by the coefficient harmonic linearization method is presented. A saturated function series approach for chaos generation. The systematic saturated function series methodicalness improved here can make multi-scroll and grid scroll chaotic attractors from a 3D linear autonomous system with a plain saturated function series supervisor. We have used a hidden bifurcation method in grid scroll., where the method of hidden bifurcation presented by Menacer, et al. in (2016) for Chua multi-scroll attractors. This additional parameter, which is absent from the initial problem, is perfectly adapted to unfold the structure of the multispiral chaotic attractor. The novelty of this article is twofold: first, the saturated function series model for hidden bifurcation in a 2 – D scroll; and second, the control of hidden bifurcation behavior by the value of the harmonic coefficient k 3 {k}_{3} .
{"title":"The behavior of hidden bifurcation in 2D scroll via saturated function series controlled by a coefficient harmonic linearization method","authors":"Zaamoune Faiza, Menacer Tidjani","doi":"10.1515/dema-2022-0211","DOIUrl":"https://doi.org/10.1515/dema-2022-0211","url":null,"abstract":"Abstract In this article, the behavior of hidden bifurcation in a two-dimensional (2D) scroll via saturated function series controlled by the coefficient harmonic linearization method is presented. A saturated function series approach for chaos generation. The systematic saturated function series methodicalness improved here can make multi-scroll and grid scroll chaotic attractors from a 3D linear autonomous system with a plain saturated function series supervisor. We have used a hidden bifurcation method in grid scroll., where the method of hidden bifurcation presented by Menacer, et al. in (2016) for Chua multi-scroll attractors. This additional parameter, which is absent from the initial problem, is perfectly adapted to unfold the structure of the multispiral chaotic attractor. The novelty of this article is twofold: first, the saturated function series model for hidden bifurcation in a 2 – D scroll; and second, the control of hidden bifurcation behavior by the value of the harmonic coefficient k 3 {k}_{3} .","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47695937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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