The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial. Moreover, we study the dual of these codes by finding their parity check polynomial.
{"title":"$lambda$-CONSTACYCLIC CODES OVER FINITE KRASNER HYPERFIELDS","authors":"M. Al Tahan, B. Davvaz","doi":"10.22190/fumi200819002a","DOIUrl":"https://doi.org/10.22190/fumi200819002a","url":null,"abstract":"The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial. Moreover, we study the dual of these codes by finding their parity check polynomial.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87728273","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 introduce the concept of classical weakly prime submodules which is the generalization of the notion of weakly classical prime submodules to modules over arbitrary noncommutative rings. We study some properties of classical weakly prime submodules and investigate their structure in different classes of modules. Also, the structure of such submodules of modules over duo rings is completely described. We investigate some properties of classical weakly prime submodules of multiplication modules.
{"title":"ON CLASSICAL WEAKLY PRIME SUBMODULES","authors":"Marziye Jamali, R. Jahani-Nezhad","doi":"10.22190/fumi200906003j","DOIUrl":"https://doi.org/10.22190/fumi200906003j","url":null,"abstract":"The aim of this paper is to introduce the concept of classical weakly prime submodules which is the generalization of the notion of weakly classical prime submodules to modules over arbitrary noncommutative rings. We study some properties of classical weakly prime submodules and investigate their structure in different classes of modules. Also, the structure of such submodules of modules over duo rings is completely described. We investigate some properties of classical weakly prime submodules of multiplication modules.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73521793","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}
Akhlidj Abdellatif, Daher Radouan, Afaf Dahani, M. El hamma
In this paper, we study two estimates useful in applications are proved for the generalized Dunkl tranform in the space $L^{p}_{alpha,Q}(mathbb{R})$ where $1frac{-1}{2}$, as applied to some classes of functions characterized by a generalized modulus of continuity and we extend two interesting E.C. Titchmarsh's theorems with the higher order at same space.
{"title":"ON ESTIMATES FOR THE GENERALIZED DUNKL TRANSFORM AND TITCHMARSH'S THEOREM IN THE SPACE $L^{p}_{alpha,Q}(mathbb{R}), (1","authors":"Akhlidj Abdellatif, Daher Radouan, Afaf Dahani, M. El hamma","doi":"10.22190/fumi200921004a","DOIUrl":"https://doi.org/10.22190/fumi200921004a","url":null,"abstract":"In this paper, we study two estimates useful in applications are proved for the generalized Dunkl tranform in the space $L^{p}_{alpha,Q}(mathbb{R})$ where $1frac{-1}{2}$, as applied to some classes of functions characterized by a generalized modulus of continuity and we extend two interesting E.C. Titchmarsh's theorems with the higher order at same space.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81047996","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 existence, uniqueness and Ulam-Hyers stability of solutions for integro-differential equations involving two fractional orders. By using Banach's fixed point theorem, we obtain some sufficient conditions for the existence and uniqueness of solution for the mentioned problem. Furthermore, we derive the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solution. At the end, an illustrative example is discussed.
{"title":"EXISTENCE AND ULAM STABILITY OF SOLUTIONS FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING TWO FRACTIONAL ORDERS","authors":"Abdelkader Saadi, M. Houas","doi":"10.22190/fumi210216009s","DOIUrl":"https://doi.org/10.22190/fumi210216009s","url":null,"abstract":"In this paper, we study existence, uniqueness and Ulam-Hyers stability of solutions for integro-differential equations involving two fractional orders. By using Banach's fixed point theorem, we obtain some sufficient conditions for the existence and uniqueness of solution for the mentioned problem. Furthermore, we derive the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solution. At the end, an illustrative example is discussed.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84935285","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 propose a numerical method for Riesz space fractional telegraph equation with time delay. The Riesz fractional telegraph equation is approximated with the interpolating polynomial P2. First a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable. Then our numerical algorithm is proposed. The convergence order and stability of the fractional order algorithms are proved. Finally, some numerical examples are constructed to describe the usefulness and profitability of the numerical method. Numerical results show that the accuracy of order O(t3).
{"title":"STABILITY AND ERROR OF THE NEW NUMERICAL SOLUTION OF FRACTIONAL RIESZ SPACE TELEGRAPH EQUATION WITH TIME DELAY","authors":"M. A. Asl, F. D. Saei, M. Javidi, Y. Mahmoudi","doi":"10.22190/fumi210401012a","DOIUrl":"https://doi.org/10.22190/fumi210401012a","url":null,"abstract":"In this paper, we propose a numerical method for Riesz space fractional telegraph equation with time delay. The Riesz fractional telegraph equation is approximated with the interpolating polynomial P2. First a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable. Then our numerical algorithm is proposed. The convergence order and stability of the fractional order algorithms are proved. Finally, some numerical examples are constructed to describe the usefulness and profitability of the numerical method. Numerical results show that the accuracy of order O(t3).","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88095357","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 give some characterizations of Frenet curves in 3-dimensional contact Lorentzian Manifolds. We define Frenet equations and the Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional contact Lorentzian Manifolds. Finally we give some corollaries and examples for these curves.
{"title":"FRENET CURVES IN 3-DIMENSIONAL CONTACT LORENTZIAN MANIFOLDS","authors":"Müslüm Aykut Akgün","doi":"10.22190/fumi210208007a","DOIUrl":"https://doi.org/10.22190/fumi210208007a","url":null,"abstract":"In this paper, we give some characterizations of Frenet curves in 3-dimensional contact Lorentzian Manifolds. We define Frenet equations and the Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional contact Lorentzian Manifolds. Finally we give some corollaries and examples for these curves.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83369472","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 study the existence and uniqueness of solutions for nonlinear fractional relaxation integro-differential equations with boundary conditions. Some results about the existence and uniqueness of solutions are established by using the Banach contraction mapping principle and the Schauder fixed point theorem. An example is provided which illustrates the theoretical results.
{"title":"EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FRACTIONAL RELAXATION INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS","authors":"Adel Lachouri, A. Ardjouni, A. Djoudi","doi":"10.22190/fumi210502016l","DOIUrl":"https://doi.org/10.22190/fumi210502016l","url":null,"abstract":"The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation integro-differential equations with boundary conditions. Some results about the existence and uniqueness of solutions are established by using the Banach contraction mapping principle and the Schauder fixed point theorem. An example is provided which illustrates the theoretical results.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85425799","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 provide several bounds for the modulus of the textit{%complex v{C}ebyv{s}ev functional}%begin{equation*}Cleft( f,gright) :=frac{1}{b-a}int_{a}^{b}fleft( tright) gleft(tright) dt-frac{1}{b-a}int_{a}^{b}fleft( tright) dtint_{a}^{b}gleft(tright) dtend{equation*}%under various assumptions for the integrable functions $f,$ $g:left[ a,b%right] rightarrow mathbb{C}$. We show amongst others that, if $f$ and $g$are absolutely continuous on $left[ a,bright] $ with $f^{prime }in L_{p}%left[ a,bright] ,$ $g^{prime }in L_{q}left[ a,bright] ,$ $p,$ $q>1$and $frac{1}{p}+frac{1}{q}=1$, then%begin{equation*}max left{ leftvert Cleft( f,gright) rightvert ,leftvert Cleft(leftvert frightvert ,gright) rightvert ,leftvert Cleft(f,leftvert grightvert right) rightvert ,leftvert Cleft( leftvertfrightvert ,leftvert grightvert right) rightvert right}end{equation*}%begin{equation*}leq left[ Cleft( ell ,F_{leftvert f^{prime }rightvert ^{p}}right) %right] ^{1/p}left[ Cleft( ell ,F_{leftvert g^{prime }rightvert^{q}}right) right] ^{1/q},end{equation*}%where $F_{leftvert hrightvert }:left[ a,bright] rightarrow mathbb{[}%0,infty )$ is defined by $F_{leftvert hrightvert }left( tright):=int_{a}^{t}$.$leftvert hleft( tright) rightvert dt$ and $ell :%left[ a,bright] rightarrow left[ a,bright] ,$ $ell left( tright) =t$is the identity function on the interval $left[ a,bright] .$ Applicationsfor the trapezoid inequality are also provided.
{"title":"SOME BOUNDS FOR THE COMPLEX µCEBYEV FUNCTIONAL OF ABSOLUTELY CONTINUOUS FUNCTIONS","authors":"S. Dragomir","doi":"10.22190/fumi210429015d","DOIUrl":"https://doi.org/10.22190/fumi210429015d","url":null,"abstract":"In this paper we provide several bounds for the modulus of the textit{%complex v{C}ebyv{s}ev functional}%begin{equation*}Cleft( f,gright) :=frac{1}{b-a}int_{a}^{b}fleft( tright) gleft(tright) dt-frac{1}{b-a}int_{a}^{b}fleft( tright) dtint_{a}^{b}gleft(tright) dtend{equation*}%under various assumptions for the integrable functions $f,$ $g:left[ a,b%right] rightarrow mathbb{C}$. We show amongst others that, if $f$ and $g$are absolutely continuous on $left[ a,bright] $ with $f^{prime }in L_{p}%left[ a,bright] ,$ $g^{prime }in L_{q}left[ a,bright] ,$ $p,$ $q>1$and $frac{1}{p}+frac{1}{q}=1$, then%begin{equation*}max left{ leftvert Cleft( f,gright) rightvert ,leftvert Cleft(leftvert frightvert ,gright) rightvert ,leftvert Cleft(f,leftvert grightvert right) rightvert ,leftvert Cleft( leftvertfrightvert ,leftvert grightvert right) rightvert right}end{equation*}%begin{equation*}leq left[ Cleft( ell ,F_{leftvert f^{prime }rightvert ^{p}}right) %right] ^{1/p}left[ Cleft( ell ,F_{leftvert g^{prime }rightvert^{q}}right) right] ^{1/q},end{equation*}%where $F_{leftvert hrightvert }:left[ a,bright] rightarrow mathbb{[}%0,infty )$ is defined by $F_{leftvert hrightvert }left( tright):=int_{a}^{t}$.$leftvert hleft( tright) rightvert dt$ and $ell :%left[ a,bright] rightarrow left[ a,bright] ,$ $ell left( tright) =t$is the identity function on the interval $left[ a,bright] .$ Applicationsfor the trapezoid inequality are also provided.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79513252","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}
Süleyman Çetinkaya, M. Bayrak, A. Demir, D. Baleanu
In this research we present two new approaches with Laplace transformation to form the truncated solution of space-time fractional differential equations (STFDE) with mixed boundary conditions. Since order of the fractional derivative of time derivative is taken between zero and one we have a sub-diffusive differential equation. First, we reduce STFDE into either a time or a space fractional differential equation which are easier to deal with. At the second step the Laplace transformation is applied to the reduced problem to obtain truncated solution. At the final step using the inverse transformations, we get the truncated solution of the problem we consider it. Presented examples illustrate the applicability and power of the approaches, used in this study.
{"title":"SOLUTIONS FOR THE FRACTIONAL MATHEMATICAL MODELS OF DIFFUSION PROCESS","authors":"Süleyman Çetinkaya, M. Bayrak, A. Demir, D. Baleanu","doi":"10.22190/fumi210218010c","DOIUrl":"https://doi.org/10.22190/fumi210218010c","url":null,"abstract":"In this research we present two new approaches with Laplace transformation to form the truncated solution of space-time fractional differential equations (STFDE) with mixed boundary conditions. Since order of the fractional derivative of time derivative is taken between zero and one we have a sub-diffusive differential equation. First, we reduce STFDE into either a time or a space fractional differential equation which are easier to deal with. At the second step the Laplace transformation is applied to the reduced problem to obtain truncated solution. At the final step using the inverse transformations, we get the truncated solution of the problem we consider it. Presented examples illustrate the applicability and power of the approaches, used in this study.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72656168","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}
We prove a unique common fixed point theorem and some coupled fixed point results satisfying generalized (ψ, θ, ϕ)-contraction on partially ordered metric spaces. With the help of results established in the first segment, we investigate the solution of periodic boundary value problems as an application. Our results improve, generalize and sharpen various well known results in the literature.
{"title":"GENERALIZED (ψ, θ, ϕ)-CONTRACTION WITH APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS","authors":"Amrish Handa","doi":"10.22190/fumi210412014h","DOIUrl":"https://doi.org/10.22190/fumi210412014h","url":null,"abstract":"We prove a unique common fixed point theorem and some coupled fixed point results satisfying generalized (ψ, θ, ϕ)-contraction on partially ordered metric spaces. With the help of results established in the first segment, we investigate the solution of periodic boundary value problems as an application. Our results improve, generalize and sharpen various well known results in the literature.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80669318","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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