Pub Date : 2023-01-01DOI: 10.46793/kgjmat2305.713h
S. REZA HEJAZI, AZADEH NADERIFARD, SOLEIMAN HOSSEINPOUR, ELHAM DASTRANJ
In the present paper Lie theory of differential equations is expanded for finding symmetry geometric vector fields of Poisson equation. Similarity variables extracted from symmetries are applied in order to find reduced forms of the considered equation by using Erdélyi-Kober operator. Conservation laws of the space-space-fractional generalized Poisson equation with the Riemann-Liouville derivative are investigated via Noether’s method. By means of the concept of non-linear self-adjointness, Noether’s operators, formal Lagrangians and conserved vectors are computed. A collocation technique is also applied to give a numerical simulation of the problem.
{"title":"Symmetries, Noether’s Theorem, Conservation Laws and Numerical Simulation for Space-Space-Fractional Generalized Poisson Equation","authors":"S. REZA HEJAZI, AZADEH NADERIFARD, SOLEIMAN HOSSEINPOUR, ELHAM DASTRANJ","doi":"10.46793/kgjmat2305.713h","DOIUrl":"https://doi.org/10.46793/kgjmat2305.713h","url":null,"abstract":"In the present paper Lie theory of differential equations is expanded for finding symmetry geometric vector fields of Poisson equation. Similarity variables extracted from symmetries are applied in order to find reduced forms of the considered equation by using Erdélyi-Kober operator. Conservation laws of the space-space-fractional generalized Poisson equation with the Riemann-Liouville derivative are investigated via Noether’s method. By means of the concept of non-linear self-adjointness, Noether’s operators, formal Lagrangians and conserved vectors are computed. A collocation technique is also applied to give a numerical simulation of the problem.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"7 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":"135843431","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}
Pub Date : 2023-01-01DOI: 10.46793/kgjmat2305.739j
JAGAN MOHAN JONNALAGADDA
In this paper, we propose sufficient conditions on existence, uniqueness and Ulam-Hyers stability of solutions for coupled systems of fractional nabla difference equations with anti-periodic boundary conditions, by using fixed point theorems. We also support these results through a couple of examples.
{"title":"Existence and Stability of Solutions for Nabla Fractional Difference Systems with Anti-periodic Boundary Conditions","authors":"JAGAN MOHAN JONNALAGADDA","doi":"10.46793/kgjmat2305.739j","DOIUrl":"https://doi.org/10.46793/kgjmat2305.739j","url":null,"abstract":"In this paper, we propose sufficient conditions on existence, uniqueness and Ulam-Hyers stability of solutions for coupled systems of fractional nabla difference equations with anti-periodic boundary conditions, by using fixed point theorems. We also support these results through a couple of examples.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"7 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":"135844176","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.857e
B. Elavarasan, Young Bae Jun
In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals and hybrid bi-ideals. We also characterize the left and right simple and the completely regular semigroups utilizing hybrid ideals and hybrid bi-ideals. We show that a semigroup S is left simple if and only if it is hybrid left simple. We also prove that if a semigroup S is intra-regular, then for each hybrid ideal ˜jµ of S, we have ˜jµ(r1r2) = ˜jµ(r2r1) for all r1, r2 ∈ S.
{"title":"Regularity of Semigroups in Terms of Hybrid Ideals and Hybrid Bi-Ideals","authors":"B. Elavarasan, Young Bae Jun","doi":"10.46793/kgjmat2206.857e","DOIUrl":"https://doi.org/10.46793/kgjmat2206.857e","url":null,"abstract":"In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals and hybrid bi-ideals. We also characterize the left and right simple and the completely regular semigroups utilizing hybrid ideals and hybrid bi-ideals. We show that a semigroup S is left simple if and only if it is hybrid left simple. We also prove that if a semigroup S is intra-regular, then for each hybrid ideal ˜jµ of S, we have ˜jµ(r1r2) = ˜jµ(r2r1) for all r1, r2 ∈ S.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45366628","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.959k
Jamal Kazemiasl, F. K. Haghani, S. Heidarian
In this paper, we present a general definition of the notion of Noetherian and Artinian BL-algebra and present a more comprehensive insight at the chain conditions in BL-algebras. We derive some theorems which generalize the existence results. We give an axiomatic approach to the notion of being Noetherian and Artinian, which is also applicable to other algebraic structures. We use a theoretical approach to define arithmetic notion that is also possible for other algebraic devices. In this study, we only focus to BL-algebras.
{"title":"A General Approach To Chain Condition in BL-Algebras","authors":"Jamal Kazemiasl, F. K. Haghani, S. Heidarian","doi":"10.46793/kgjmat2206.959k","DOIUrl":"https://doi.org/10.46793/kgjmat2206.959k","url":null,"abstract":"In this paper, we present a general definition of the notion of Noetherian and Artinian BL-algebra and present a more comprehensive insight at the chain conditions in BL-algebras. We derive some theorems which generalize the existence results. We give an axiomatic approach to the notion of being Noetherian and Artinian, which is also applicable to other algebraic structures. We use a theoretical approach to define arithmetic notion that is also possible for other algebraic devices. In this study, we only focus to BL-algebras.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43354041","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.981h
R. Hafez, Youssri Hassan Youssri
In this paper, the shifted Gegenbauer-Gauss collocation (SGGC) method is applied to fractional neutral functional-differential equations with proportional delays. The technique we have used is based on shifted Gegenbauer polynomials and Gauss quadrature integration. The shifted Gegenbauer-Gauss method reduces solving the generalized fractional pantograph equation fractional neutral functional-differential equations to a system of algebraic equations. Reasonable numerical results are obtained by selecting few shifted Gegenbauer-Gauss collocation points. Numerical results demonstrate its accuracy, and versatility of the proposed techniques.
{"title":"Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays","authors":"R. Hafez, Youssri Hassan Youssri","doi":"10.46793/kgjmat2206.981h","DOIUrl":"https://doi.org/10.46793/kgjmat2206.981h","url":null,"abstract":"In this paper, the shifted Gegenbauer-Gauss collocation (SGGC) method is applied to fractional neutral functional-differential equations with proportional delays. The technique we have used is based on shifted Gegenbauer polynomials and Gauss quadrature integration. The shifted Gegenbauer-Gauss method reduces solving the generalized fractional pantograph equation fractional neutral functional-differential equations to a system of algebraic equations. Reasonable numerical results are obtained by selecting few shifted Gegenbauer-Gauss collocation points. Numerical results demonstrate its accuracy, and versatility of the proposed techniques.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42097548","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.895r
R. Ramalakshmi, K. Kathiresan
We introduce a new graph characteristic, the total absolute difference edge irregularity strength. We obtain the estimation on the total absolute difference edge irregularity strength and determine the precise values for some families of graphs.
{"title":"Total Absolute Difference Edge Irregularity Strength of Graphs","authors":"R. Ramalakshmi, K. Kathiresan","doi":"10.46793/kgjmat2206.895r","DOIUrl":"https://doi.org/10.46793/kgjmat2206.895r","url":null,"abstract":"We introduce a new graph characteristic, the total absolute difference edge irregularity strength. We obtain the estimation on the total absolute difference edge irregularity strength and determine the precise values for some families of graphs.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49352527","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.841d
C. Derbazi
This paper is devoted to the existence of solutions for certain classes of nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis is based on Darbo’s fixed point theorem in conjunction with the technique of Hausdorff measure of noncompactness. An example is also presented to illustrate the effectiveness of the main results.
{"title":"Nonlinear Sequential Caputo and Caputo-Hadamard Fractional Differential Equations with Dirichlet Boundary Conditions in Banach Spaces","authors":"C. Derbazi","doi":"10.46793/kgjmat2206.841d","DOIUrl":"https://doi.org/10.46793/kgjmat2206.841d","url":null,"abstract":"This paper is devoted to the existence of solutions for certain classes of nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis is based on Darbo’s fixed point theorem in conjunction with the technique of Hausdorff measure of noncompactness. An example is also presented to illustrate the effectiveness of the main results.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70588785","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.929r
M. Rahimi, S. Karbassi, M. R. Hooshmandasl
In this work, two-dimensional time-dependent quantum equation problems are studied. We introduce a numerical algorithm for solving the two-dimensional nonlinear complex quantum system with MLS and FDM methods. An efficient and accurate computational algorithm based on both, the moving least squares (MLS) and the finite difference (FDM) methods is proposed for solving it. The results demonstrate that the proposed algorithm is a robust algorithm with good accuracy. This is developed on MLS and FDM methods using numerical simulation for solving these kind of problems.
{"title":"Numerical Solution of Shrödinger Equations Based on the Meshless Methods","authors":"M. Rahimi, S. Karbassi, M. R. Hooshmandasl","doi":"10.46793/kgjmat2206.929r","DOIUrl":"https://doi.org/10.46793/kgjmat2206.929r","url":null,"abstract":"In this work, two-dimensional time-dependent quantum equation problems are studied. We introduce a numerical algorithm for solving the two-dimensional nonlinear complex quantum system with MLS and FDM methods. An efficient and accurate computational algorithm based on both, the moving least squares (MLS) and the finite difference (FDM) methods is proposed for solving it. The results demonstrate that the proposed algorithm is a robust algorithm with good accuracy. This is developed on MLS and FDM methods using numerical simulation for solving these kind of problems.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43502037","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.905s
K. Y. N. Sayar, A. Bergam
In this paper, we investigate some stability and hyperstability results for the following Cauchy-Jensen functional equation fx+y 2+fx−y 2=f(x) in (2,α)-Banach spaces using Brzd¸ek and Ciepliński’s fixed point approach.
{"title":"Stability of Cauchy-Jensen Type Functional Equation in (2, α)–Banach Spaces","authors":"K. Y. N. Sayar, A. Bergam","doi":"10.46793/kgjmat2206.905s","DOIUrl":"https://doi.org/10.46793/kgjmat2206.905s","url":null,"abstract":"In this paper, we investigate some stability and hyperstability results for the following Cauchy-Jensen functional equation fx+y 2+fx−y 2=f(x) in (2,α)-Banach spaces using Brzd¸ek and Ciepliński’s fixed point approach.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46185904","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}
Pub Date : 2022-12-01DOI: 10.46793/kgjmat2206.919u
A. Uçum, K. Ilarslan
In the present paper, we give the notion of k-type bi-null Cartan slant helices in R6 2, where k ∈ {1,2,3,4,5,6}. We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions.
{"title":"k-TYPE BI-NULL CARTAN SLANT HELICES IN R6 2","authors":"A. Uçum, K. Ilarslan","doi":"10.46793/kgjmat2206.919u","DOIUrl":"https://doi.org/10.46793/kgjmat2206.919u","url":null,"abstract":"In the present paper, we give the notion of k-type bi-null Cartan slant helices in R6 2, where k ∈ {1,2,3,4,5,6}. We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45967583","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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