Pub Date : 2023-09-01DOI: 10.32513/asetmj/193220082328
Zhen Wang
In this paper, we consider the efficient numerical approach for the time-fractional convection-diffusion equation with Caputo-Hadamard derivative. This method uses the nonuniform L2-1$_sigma$ formula for the time-fractional derivative and the local discontinuous Galerkin (LDG) method for the space approximation. In order to analyze the stability and convergence of the algorithm, a new discrete Gronwall inequality related to the discretized model with Caputo-Hadamard derivative is established. The result shows that the method has $alpha$-robust, i.e., it remains valid when $alpharightarrow 1^-$. Finally, the theoretical results are further verified by a numerical example.
{"title":"A nonuniform L2-1$_sigma$/LDG method for the Caputo-Hadamard time-fractional convection-diffusion equation","authors":"Zhen Wang","doi":"10.32513/asetmj/193220082328","DOIUrl":"https://doi.org/10.32513/asetmj/193220082328","url":null,"abstract":"In this paper, we consider the efficient numerical approach for the time-fractional convection-diffusion equation with Caputo-Hadamard derivative. This method uses the nonuniform L2-1$_sigma$ formula for the time-fractional derivative and the local discontinuous Galerkin (LDG) method for the space approximation. In order to analyze the stability and convergence of the algorithm, a new discrete Gronwall inequality related to the discretized model with Caputo-Hadamard derivative is established. The result shows that the method has $alpha$-robust, i.e., it remains valid when $alpharightarrow 1^-$. Finally, the theoretical results are further verified by a numerical example.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135889414","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 : 2023-09-01DOI: 10.32513/asetmj/193220082324
Buddhadev Pal, Santosh Kumar
In this paper, we study the geometry of the proper curve and proper helix of order 2 lying on the hyperbolic plane $H_{0}^2(-r)$, globally from Minkowski space $E_{1}^3$. We develop the Frenet frame (orthogonal frame) along the proper curve of order 2 using connection $tilde{nabla}$ on $E_ {1}^3$ and connection $nabla$ on $H_ {0} ^ 2(-r)$. The Frenet frame for the proper curve and proper helix of order 2 depends on the curvature of the proper curve and proper helix of order 2 in the hyperbolic plane $ H_ {0} ^ 2(-r)$. Finally, we find the condition for a proper curve of order 2 with non constant curvature to become a $V_{k} -$slant helix in $E_{1}^3$.
{"title":"Global view of curves lying on $H_{0}^2(-r) subset E_{1}^3$","authors":"Buddhadev Pal, Santosh Kumar","doi":"10.32513/asetmj/193220082324","DOIUrl":"https://doi.org/10.32513/asetmj/193220082324","url":null,"abstract":"In this paper, we study the geometry of the proper curve and proper helix of order 2 lying on the hyperbolic plane $H_{0}^2(-r)$, globally from Minkowski space $E_{1}^3$. We develop the Frenet frame (orthogonal frame) along the proper curve of order 2 using connection $tilde{nabla}$ on $E_ {1}^3$ and connection $nabla$ on $H_ {0} ^ 2(-r)$. The Frenet frame for the proper curve and proper helix of order 2 depends on the curvature of the proper curve and proper helix of order 2 in the hyperbolic plane $ H_ {0} ^ 2(-r)$. Finally, we find the condition for a proper curve of order 2 with non constant curvature to become a $V_{k} -$slant helix in $E_{1}^3$.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427937","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 : 2023-09-01DOI: 10.32513/asetmj/193220082326
Ravi Kumar, Sunil K. Sharma
In this paper we define asymptotically lacunary statistical equivalence set sequences of order $(alpha,beta)$ and studied some properties of this concept. We also make an effort to define strongly asymptotically lacunary $p$-equivalence and strongly Cesaro asymptotically $p$-equivalence of order $(alpha,beta)$ and examine some topological properties.
{"title":"Asymptotically lacunary statistical equivalence set sequences of order $(alpha,beta)$}","authors":"Ravi Kumar, Sunil K. Sharma","doi":"10.32513/asetmj/193220082326","DOIUrl":"https://doi.org/10.32513/asetmj/193220082326","url":null,"abstract":"In this paper we define asymptotically lacunary statistical equivalence set sequences of order $(alpha,beta)$ and studied some properties of this concept. We also make an effort to define strongly asymptotically lacunary $p$-equivalence and strongly Cesaro asymptotically $p$-equivalence of order $(alpha,beta)$ and examine some topological properties.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427936","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 : 2023-09-01DOI: 10.32513/asetmj/193220082327
Abderrahim Guerfi, Abdelouaheb Ardjoun
The objective of this paper is to present the existence of positive periodic solutions of nonlinear neutral dynamic equations on periodic time scales by applying the Krasnoselskii fixed point theorem. Our findings combine the well-known discrete and continuous cases
{"title":"Positive periodic solutions of a first order neutral dynamic equation on periodic time scales","authors":"Abderrahim Guerfi, Abdelouaheb Ardjoun","doi":"10.32513/asetmj/193220082327","DOIUrl":"https://doi.org/10.32513/asetmj/193220082327","url":null,"abstract":"The objective of this paper is to present the existence of positive periodic solutions of nonlinear neutral dynamic equations on periodic time scales by applying the Krasnoselskii fixed point theorem. Our findings combine the well-known discrete and continuous cases","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427939","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 : 2023-09-01DOI: 10.32513/asetmj/193220082323
Laia Tugores
The aim of this note is to introduce a topic about some ways to interpolate values of a function, on a finite set of points in the disk. Each interpolating function is built by means of a certain distance between points. We study the behaviour of such interpolations.
{"title":"Finite interpolation by distances in the disk","authors":"Laia Tugores","doi":"10.32513/asetmj/193220082323","DOIUrl":"https://doi.org/10.32513/asetmj/193220082323","url":null,"abstract":"The aim of this note is to introduce a topic about some ways to interpolate values of a function, on a finite set of points in the disk. Each interpolating function is built by means of a certain distance between points. We study the behaviour of such interpolations.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427934","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 : 2023-09-01DOI: 10.32513/asetmj/193220082325
Yogesh M. Thakkar, Ajay K. Shukla
{"title":"Some formulas for the function ${R_3}left[ {mu,mu',delta,delta';gamma;upsilon ,tau ,{z_1},{z_2}} right]$","authors":"Yogesh M. Thakkar, Ajay K. Shukla","doi":"10.32513/asetmj/193220082325","DOIUrl":"https://doi.org/10.32513/asetmj/193220082325","url":null,"abstract":"","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427935","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 : 2023-09-01DOI: 10.32513/asetmj/193220082329
Loubna Boulkemh, Doria Affan
In this paper, we consider a class of first-order differential inclusion, the right-hand side of the problem is governed by the so-called nonconvex state-dependent sweeping process. The perturbation, known as the external forces applied on the system, is general and takes the form of a sum of a single-valued mapping depends on velocity and a set-valued mapping depends on state. We study the existence of solutions and the compactness of the attainable set, where the set-valued mapping is an upper semi-continuous with convex values. Then, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. The results obtained are applied to the study of a control problem.
{"title":"Perturbed state-dependent sweeping processes","authors":"Loubna Boulkemh, Doria Affan","doi":"10.32513/asetmj/193220082329","DOIUrl":"https://doi.org/10.32513/asetmj/193220082329","url":null,"abstract":"In this paper, we consider a class of first-order differential inclusion, the right-hand side of the problem is governed by the so-called nonconvex state-dependent sweeping process. The perturbation, known as the external forces applied on the system, is general and takes the form of a sum of a single-valued mapping depends on velocity and a set-valued mapping depends on state. We study the existence of solutions and the compactness of the attainable set, where the set-valued mapping is an upper semi-continuous with convex values. Then, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. The results obtained are applied to the study of a control problem.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427938","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 : 2023-09-01DOI: 10.32513/asetmj/193220082322
Shagun Banga, S. Sivaprasad Kumar
In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new subclass $mathcal{S}^*(phi)$ by considering a specific function in place of $phi$, which is the solution of a differential subordination obtained by reformulating a differential inequality. We also study the class defined by means of a differential inequality and establish the relation between this class and $mathcal{S}^*(phi)$. We obtain certain inclusion and radius results for both the classes. Further, we estimate logarithmic coefficients, inverse coefficients and Fekete-Szeg"o functional bounds for functions in $ mathcal{S}^*(phi)$.
{"title":"A novel subclass of starlike functions","authors":"Shagun Banga, S. Sivaprasad Kumar","doi":"10.32513/asetmj/193220082322","DOIUrl":"https://doi.org/10.32513/asetmj/193220082322","url":null,"abstract":"In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new subclass $mathcal{S}^*(phi)$ by considering a specific function in place of $phi$, which is the solution of a differential subordination obtained by reformulating a differential inequality. We also study the class defined by means of a differential inequality and establish the relation between this class and $mathcal{S}^*(phi)$. We obtain certain inclusion and radius results for both the classes. Further, we estimate logarithmic coefficients, inverse coefficients and Fekete-Szeg\"o functional bounds for functions in $ mathcal{S}^*(phi)$.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135427940","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 : 2023-03-01DOI: 10.32513/asetmj/193220082321
Yakaiah K., Sharma R. Bharavi, K. Ganesh, K. Saroja
The aim of the present paper is to find the fourth Hankel and Toeplitz determinants for bounded turning functions subordinate to $1+tanhz$. We also consider this problem for Fekete-Szego inequality and Zalcman Conjectures for bounded turning functions subordinate to $1+tanhz$.
{"title":"Fourth Hankel and Toeplitz determinants for bounded turning functions subordinate to $1+tanhz$","authors":"Yakaiah K., Sharma R. Bharavi, K. Ganesh, K. Saroja","doi":"10.32513/asetmj/193220082321","DOIUrl":"https://doi.org/10.32513/asetmj/193220082321","url":null,"abstract":"The aim of the present paper is to find the fourth Hankel and Toeplitz determinants for bounded turning functions subordinate to $1+tanhz$. We also consider this problem for Fekete-Szego inequality and Zalcman Conjectures for bounded turning functions subordinate to $1+tanhz$.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135532387","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 : 2023-03-01DOI: 10.32513/asetmj/19322008237
B. Venkateswarlu, P. Thirupathi Reddy, Chao Meng, G. Swapna
In this work, we introduce and investigate a new class k−U˜Ssm(λ,γ,t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.
{"title":"On a certain subclass of analytic functions defined by a differential operator","authors":"B. Venkateswarlu, P. Thirupathi Reddy, Chao Meng, G. Swapna","doi":"10.32513/asetmj/19322008237","DOIUrl":"https://doi.org/10.32513/asetmj/19322008237","url":null,"abstract":"In this work, we introduce and investigate a new class k−U˜Ssm(λ,γ,t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.","PeriodicalId":484498,"journal":{"name":"Advanced Studies Euro-Tbilisi Mathematical Journal","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135185301","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：