Infectious diseases spread by microorganisms, viruses and bacteria, which can be transmitted from individual to individual very quickly and adversely affect public health, need to be treated immediately. In order to eliminate the structures that are harmful to the body or to strengthen the immune system, which is the whole of cells, structures and processes, individuals are vaccinated and the disease is suppressed. Thus, communicable diseases are prevented from threatening public health significantly. This paper offers a nonlinear fractional order system for modeling the effects of vaccination on a SVIR infectious disease. To see the memory effect on the system parameters, the model defined by the ordinary differential equation is redefined with the Caputo fractional derivative. Afterwards, the stability analysis and explanations are given about the fractional infectious disease SVIR model, the existence and uniqueness of the system are made. When $R^{c}<1$, it is seen that the disease is under control by vaccination, through the figures obtained with the help of MATLAB for the fractional SVIR model.
{"title":"DYNAMIC ANALYSIS OF A FRACTIONAL SVIR SYSTEM MODELING AN INFECTIOUS DISEASE","authors":"Necati Ozdemir, Esmehan Uçar, D. Avcı","doi":"10.22190/fumi211020042o","DOIUrl":"https://doi.org/10.22190/fumi211020042o","url":null,"abstract":"Infectious diseases spread by microorganisms, viruses and bacteria, which can be transmitted from individual to individual very quickly and adversely affect public health, need to be treated immediately. In order to eliminate the structures that are harmful to the body or to strengthen the immune system, which is the whole of cells, structures and processes, individuals are vaccinated and the disease is suppressed. Thus, communicable diseases are prevented from threatening public health significantly. This paper offers a nonlinear fractional order system for modeling the effects of vaccination on a SVIR infectious disease. To see the memory effect on the system parameters, the model defined by the ordinary differential equation is redefined with the Caputo fractional derivative. Afterwards, the stability analysis and explanations are given about the fractional infectious disease SVIR model, the existence and uniqueness of the system are made. When $R^{c}<1$, it is seen that the disease is under control by vaccination, through the figures obtained with the help of MATLAB for the fractional SVIR model.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88631602","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}
In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{Delta_{beta}^{tilde{alpha}}},f)-$ statistical convergence, $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ statistical Cauchy and p-strongly $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ Cesàro summability, $(0
{"title":"ON f− STATİSTİCAL CONVERGENCE OF FRACTİONAL DİFFERENCE ON DOUBLE SEQUENCES","authors":"Koray İbrahim Atabey, Muhammed Çinar","doi":"10.22190/fumi211029044a","DOIUrl":"https://doi.org/10.22190/fumi211029044a","url":null,"abstract":"In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{Delta_{beta}^{tilde{alpha}}},f)-$ statistical convergence, $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ statistical Cauchy and p-strongly $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ Cesàro summability, $(0<p<infty)$ for double sequences. We also give some inclusion relations between $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ statistical convergence and p-strongly $({}^{}_{2}{Delta^{tilde{alpha}}},f)-$ Cesàro summability $(0<p<infty)$.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81667233","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}
The purpose of this article is to introduce a new subclass of analytic and bi-univalent functions, in associated with sigmoid function and to investigate the upper bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szego inequalities for this subclass of the bi-univalent function class sigma. We also give several illustrative examples of the bi-univalent functionclass which we introduce here.
{"title":"THE FEKETE-SZEGO PROBLEMS FOR SUBCLASS OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH SIGMOID FUNCTION","authors":"H. Orhan, G. Murugusundaramoorthy, M. Çağlar","doi":"10.22190/fumi201022034o","DOIUrl":"https://doi.org/10.22190/fumi201022034o","url":null,"abstract":"The purpose of this article is to introduce a new subclass of analytic and bi-univalent functions, in associated with sigmoid function and to investigate the upper bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szego inequalities for this subclass of the bi-univalent function class sigma. We also give several illustrative examples of the bi-univalent functionclass which we introduce here.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90251479","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}
The statistical unbounded topological convergence was studied and investigated with respect to the solid topology in locally solid Riesz spaces. In this paper, we introduce the statistical unbounded order convergence in Riesz spaces by developing a topology-free technique with the order convergence on Riesz spaces. Moreover, we give some relations with other kinds of statistical convergences.
{"title":"STATISTICAL UNBOUNDED ORDER CONVERGENCE IN RIESZ SPACES","authors":"A. Aydın","doi":"10.22190/fumi211013040a","DOIUrl":"https://doi.org/10.22190/fumi211013040a","url":null,"abstract":"The statistical unbounded topological convergence was studied and investigated with respect to the solid topology in locally solid Riesz spaces. In this paper, we introduce the statistical unbounded order convergence in Riesz spaces by developing a topology-free technique with the order convergence on Riesz spaces. Moreover, we give some relations with other kinds of statistical convergences.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81742128","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}
Archana Dewangan, A. K. Dubey, U. Mishra, R. Dubey
In this paper, we establish the existence and uniqueness of a fixed point of (α, β)-admissible almost z-contractions via simulation functions in metric-like spaces. Our results generalize and unify several fixed point theorem in literature.
{"title":"FIXED POINT RESULTS FOR (α − β)-ADMISSIBLE ALMOST z-CONTRACTIONS IN METRIC-LIKE SPACE VIA SIMULATION FUNCTION","authors":"Archana Dewangan, A. K. Dubey, U. Mishra, R. Dubey","doi":"10.22190/fumi210705037d","DOIUrl":"https://doi.org/10.22190/fumi210705037d","url":null,"abstract":"In this paper, we establish the existence and uniqueness of a fixed point of (α, β)-admissible almost z-contractions via simulation functions in metric-like spaces. Our results generalize and unify several fixed point theorem in literature.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77460891","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}
In this paper, we introduce a new concept $k$-$beta $-convex functions and establish some new Hermite-Hadamard type inequalities for functions whose derivative modulus is $k$-$beta $-convex via $k$-fractional conformable integral operators.
{"title":"NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR $k$-$beta $-CONVEX FUNCTIONS VIA GENERALIZED $k$-FRACTIONAL CONFORMABLE INTEGRAL OPERATORS","authors":"F. Lakhal, Meftah Badreddine","doi":"10.22190/fumi211001039l","DOIUrl":"https://doi.org/10.22190/fumi211001039l","url":null,"abstract":"In this paper, we introduce a new concept $k$-$beta $-convex functions and establish some new Hermite-Hadamard type inequalities for functions whose derivative modulus is $k$-$beta $-convex via $k$-fractional conformable integral operators.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85346143","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}
In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.
{"title":"ON BOUNDEDNESS WITH SPEED λ IN ULTRAMETRIC FIELDS","authors":"Natarajan Narayanasubramanian Pinnangudi","doi":"10.22190/fumi211031045p","DOIUrl":"https://doi.org/10.22190/fumi211031045p","url":null,"abstract":"In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81260895","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}
In this paper we study a variable-exponent fourth-order viscoelastic equation of the form$$|u_{t}|^{rho(x)}u_{tt}+Delta[(a+b|Delta u|^{m(x)-2})Delta u]-int_{0}^{t}g(t-s)Delta^{2}u(s)ds=|u|^{p(x)-2}u,$$in a bounded domain of $R^{n}$. Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the on by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M).
{"title":"EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK","authors":"M. Shahrouzi","doi":"10.22190/fumi210222035s","DOIUrl":"https://doi.org/10.22190/fumi210222035s","url":null,"abstract":"In this paper we study a variable-exponent fourth-order viscoelastic equation of the form$$|u_{t}|^{rho(x)}u_{tt}+Delta[(a+b|Delta u|^{m(x)-2})Delta u]-int_{0}^{t}g(t-s)Delta^{2}u(s)ds=|u|^{p(x)-2}u,$$in a bounded domain of $R^{n}$. Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the on by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M).","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81144999","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}
The aim of this paper is to establish some relationship between the set of strong uniform statistical cluster points and the set of strong statistical cluster points of a given sequence in the probabilistic normed space. To this aim, let the uniform density be on the positive integers N for a sequence in the probabilistic normed space, that is, cases as equal of the lower and upper uniform density of a subset of N. We introduce the concept of strong uniform statistical cluster points and give a new type convergence in the probabilistic normed space. Note that the set of strong uniform statistical cluster points is a non-empty compact set. We also investigate some properties of the set all strong uniform cluster points of a sequence in the probabilistic normed space.
{"title":"SOME PROPERTIES OF THE SET OF ALL STRONG UNIFORM CLUSTER POINTS","authors":"S. Pehlivan","doi":"10.22190/fumi211017041p","DOIUrl":"https://doi.org/10.22190/fumi211017041p","url":null,"abstract":"The aim of this paper is to establish some relationship between the set of strong uniform statistical cluster points and the set of strong statistical cluster points of a given sequence in the probabilistic normed space. To this aim, let the uniform density be on the positive integers N for a sequence in the probabilistic normed space, that is, cases as equal of the lower and upper uniform density of a subset of N. We introduce the concept of strong uniform statistical cluster points and give a new type convergence in the probabilistic normed space. Note that the set of strong uniform statistical cluster points is a non-empty compact set. We also investigate some properties of the set all strong uniform cluster points of a sequence in the probabilistic normed space.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84446676","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}
The relation between of fuzzy subsets and classical mathematics is fundamental to extend of new approchs in applied mathematics. This paper, applies the concept of fuzzy metric on construction of fuzzy Hausdorff space and fuzzy manifold space. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces. This study, extends the concept of fuzzy metric space to union and product of fuzzy metric spaces and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. Valued-level subsets play the main role in the connection of the notation of manifolds and fuzzy metrics.
{"title":"APPLICATION OF FUZZY METRIC ON MANIFOLDS","authors":"M. Hamidi, Mahdi Mollaei Arani","doi":"10.22190/fumi200709032h","DOIUrl":"https://doi.org/10.22190/fumi200709032h","url":null,"abstract":"The relation between of fuzzy subsets and classical mathematics is fundamental to extend of new approchs in applied mathematics. This paper, applies the concept of fuzzy metric on construction of fuzzy Hausdorff space and fuzzy manifold space. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces. This study, extends the concept of fuzzy metric space to union and product of fuzzy metric spaces and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. Valued-level subsets play the main role in the connection of the notation of manifolds and fuzzy metrics.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77737159","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}
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