In this study, an exact and a numerical method namely direct algebraic method and collocation finite element method are proposed for solving soliton solutions of a special form of fifth-order KdV (fKdV) equation that is of particular importance: Caudrey-Dodd-Gibbon (CDG) equation. For these aims, homogeneous balance method and septic B-spline functions are used for exact and numerical solutions, respectively. Next, it is proved by applying von-Neumann stability analysis that the numerical method is unconditionally stable. The error norms $L_{2}$ and $L_{infty }$ have been computed to control proficiency and conservation properties of the suggested algorithm. The obtained numerical results have been listed in the tables. The graphs are modelled so that easy visualization of properties of the problem. Also, the obtained results indicate that our method is favourable for solving such problems.
{"title":"New Exact and Numerical Experiments for the Caudrey-Dodd-Gibbon Equation","authors":"Seydi Battal Gazi Karakoç, Derya Yıldırım Sucu","doi":"10.33401/fujma.1389595","DOIUrl":"https://doi.org/10.33401/fujma.1389595","url":null,"abstract":"In this study, an exact and a numerical method namely direct algebraic method and collocation finite element method are proposed for solving soliton solutions of a special form of fifth-order KdV (fKdV) equation that is of particular importance: Caudrey-Dodd-Gibbon (CDG) equation. For these aims, homogeneous balance method and septic B-spline functions are used for exact and numerical solutions, respectively. Next, it is proved by applying von-Neumann stability analysis that the numerical method is unconditionally stable. The error norms $L_{2}$ and $L_{infty }$ have been computed to control proficiency and conservation properties of the suggested algorithm. The obtained numerical results have been listed in the tables. The graphs are modelled so that easy visualization of properties of the problem. Also, the obtained results indicate that our method is favourable for solving such problems.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140387188","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 authors present an integral widening of operators which preserve affine functions. Influenced by the operators which preserve affine functions, we define the integral extension of these operators. We give quantitative type theorem using weighted modulus of continuity. Withal quantitative Voronovskaya theorem is aquired by classical modulus of continuity. When the moments of the operator are known, convergence results with the moments obtained for the Kantorovich form of the same operator is given.
{"title":"A Note On Kantorovich Type Operators Which Preserve Affine Functions","authors":"Didem Aydın Arı, Gizem Uğur Yılmaz","doi":"10.33401/fujma.1424382","DOIUrl":"https://doi.org/10.33401/fujma.1424382","url":null,"abstract":"The authors present an integral widening of operators which preserve affine functions. Influenced by the operators which preserve affine functions, we define the integral extension of these operators. We give quantitative type theorem using weighted modulus of continuity. Withal quantitative Voronovskaya theorem is aquired by classical modulus of continuity. When the moments of the operator are known, convergence results with the moments obtained for the Kantorovich form of the same operator is given.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"28 52","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140395891","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 article, some mathematical properties of $left( iota ,x_{0}right) $-generalized logistic-type function are presented. This four-parameter generalized function can be considered as a statistical phenomenon enhancing more vigorous survival analysis models. Moreover, the behaviors of the relevant parametric functions obtained are examined with graphics using computer programming language Python 3.9.
{"title":"On an $left( iota ,x_{0}right) $-Generalized Logistic-Type Function","authors":"Seda Karateke","doi":"10.33401/fujma.1423906","DOIUrl":"https://doi.org/10.33401/fujma.1423906","url":null,"abstract":"In this article, some mathematical properties of $left( iota ,x_{0}right) $-generalized logistic-type function are presented. This four-parameter generalized function can be considered as a statistical phenomenon enhancing more vigorous survival analysis models. Moreover, the behaviors of the relevant parametric functions obtained are examined with graphics using computer programming language Python 3.9.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"23 1‐2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140398044","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}
This article deals with the qualitative analysis of a general class of difference equations. That is, we examine the periodicity nature and the stability character of some non-linear second-order difference equations. Homogeneous functions are used while examining the character of the solutions of introduced difference equations. Moreover, a new technique available in the literature is used to examine the periodic solutions of these equations.
{"title":"The Qualitative Analysis of Some Difference Equations Using Homogeneous Functions","authors":"Mehmet Gümüş, Şeyma Irmak Eği̇lmez","doi":"10.33401/fujma.1336964","DOIUrl":"https://doi.org/10.33401/fujma.1336964","url":null,"abstract":"This article deals with the qualitative analysis of a general class of difference equations. That is, we examine the periodicity nature and the stability character of some non-linear second-order difference equations. Homogeneous functions are used while examining the character of the solutions of introduced difference equations. Moreover, a new technique available in the literature is used to examine the periodic solutions of these equations.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"30 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139172251","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 construct a new sequence of Sz'{a}sz-Mirakjan Kantorovich Operators $K_{n,gamma}(f;x)$ depending on a parameter $gamma$. We prove direct and local approximation properties of these operators. We obtain the operators $K_{n,gamma}(f;x)$ to have better approximation results than classical Sz'{a}sz-Mirakjan Kantorovich Operators for all $xin[0,infty)$, for any $gamma>1$. Furthermore, we investigate the approximation results of these operators graphically and numerically. Moreover, we introduce new operators from $K_{n,gamma}(f;x)$ that preserve affine functions and bivariate case of $K_{n,gamma}(f;x)$. Then, we study their approximation properties and also illustrate the convergence of these new operators comparing with their classical cases.
{"title":"A New Generalization of Szasz-Mirakjan Kantorovich Operators for Better Error Estimation","authors":"Erdem BAYTUNÇ, Hüseyin AKTUĞLU, Nazım MAHMUDOV","doi":"10.33401/fujma.1355254","DOIUrl":"https://doi.org/10.33401/fujma.1355254","url":null,"abstract":"In this paper, we construct a new sequence of Sz'{a}sz-Mirakjan Kantorovich Operators $K_{n,gamma}(f;x)$ depending on a parameter $gamma$. We prove direct and local approximation properties of these operators. We obtain the operators $K_{n,gamma}(f;x)$ to have better approximation results than classical Sz'{a}sz-Mirakjan Kantorovich Operators for all $xin[0,infty)$, for any $gamma>1$. Furthermore, we investigate the approximation results of these operators graphically and numerically. Moreover, we introduce new operators from $K_{n,gamma}(f;x)$ that preserve affine functions and bivariate case of $K_{n,gamma}(f;x)$. Then, we study their approximation properties and also illustrate the convergence of these new operators comparing with their classical cases.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"4 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135972834","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}
With this work, we present the asymptotical strongly $p$-deferred invariant and asymptotical deferred invariant statistical equivalence of order $alpha$ ($0
{"title":"Wijsman Deferred Invariant Statistical and Strong $p$-Deferred Invariant Equivalence of Order $alpha$","authors":"Esra GÜLLE, Uğur ULUSU","doi":"10.33401/fujma.1364368","DOIUrl":"https://doi.org/10.33401/fujma.1364368","url":null,"abstract":"With this work, we present the asymptotical strongly $p$-deferred invariant and asymptotical deferred invariant statistical equivalence of order $alpha$ ($0","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"12 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136017631","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}
This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density. Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map. Three models from the literature are considered to simulate the results. The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.
{"title":"Set-Valued Stabilization of Reaction-Diffusion Model by Chemotherapy and or Radiotherapy","authors":"Amine MOUSTAFİD","doi":"10.33401/fujma.1299982","DOIUrl":"https://doi.org/10.33401/fujma.1299982","url":null,"abstract":"This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density. Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map. Three models from the literature are considered to simulate the results. The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136276640","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}
A simplicial commutative algebra with Moore complex of length 1 gives a crossed module structure over commutative algebras. In this study, we will give 2-dimensional version of this result by giving hypercrossed complex pairings for a bisimplicial algebra and its Moore bicomplex. We give a detailed calculation in low dimensions for these pairings to see their role in the structures of crossed squares and bisimplicial algebras. In this context, we prove that if the Moore bicomplex of a bisimplicial commutative algebra is of length 1, then it gives a crossed square structure over commutative algebras.
{"title":"Bisimplicial Commutative Algebras and Crossed Squares","authors":"Özgün GÜRMEN ALANSAL, Erdal ULUALAN","doi":"10.33401/fujma.1292885","DOIUrl":"https://doi.org/10.33401/fujma.1292885","url":null,"abstract":"A simplicial commutative algebra with Moore complex of length 1 gives a crossed module structure over commutative algebras. In this study, we will give 2-dimensional version of this result by giving hypercrossed complex pairings for a bisimplicial algebra and its Moore bicomplex. We give a detailed calculation in low dimensions for these pairings to see their role in the structures of crossed squares and bisimplicial algebras. In this context, we prove that if the Moore bicomplex of a bisimplicial commutative algebra is of length 1, then it gives a crossed square structure over commutative algebras.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136278149","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 present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by Gorka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution.
{"title":"Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space","authors":"Serkan İLTER","doi":"10.33401/fujma.1333804","DOIUrl":"https://doi.org/10.33401/fujma.1333804","url":null,"abstract":"In this paper, we present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by Gorka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136344929","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}
Bi-flux diffusion equation, can be easily affected by the existence of external factors, is known as an anomalous diffusion. In this paper, the inverse problem (IP) of determining the solely time-dependent zero-order coefficient in a linear Bi-flux diffusion equation with initial and homogeneous boundary conditions from an integral additional specification of the energy is considered. The unique solvability of the inverse problem is demonstrated by using the contraction principle for sufficiently small times.
{"title":"Identification of the Solely Time-Dependent Zero-Order Coefficient in a Linear Bi-Flux Diffusion Equation from an Integral Measurement","authors":"İbrahim TEKİN, Mehmet Akif ÇETİN","doi":"10.33401/fujma.1248680","DOIUrl":"https://doi.org/10.33401/fujma.1248680","url":null,"abstract":"Bi-flux diffusion equation, can be easily affected by the existence of external factors, is known as an anomalous diffusion. In this paper, the inverse problem (IP) of determining the solely time-dependent zero-order coefficient in a linear Bi-flux diffusion equation with initial and homogeneous boundary conditions from an integral additional specification of the energy is considered. The unique solvability of the inverse problem is demonstrated by using the contraction principle for sufficiently small times.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136278150","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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