Pub Date : 2020-09-01DOI: 10.32513/tbilisi/1601344905
M. Monsef, H. Doostie
{"title":"Classes of non-commutative semigroups with finite Fibonacci invariants","authors":"M. Monsef, H. Doostie","doi":"10.32513/tbilisi/1601344905","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344905","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"153-159"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42183433","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344896
Chenkuan Li, Changpin Li
The goal of this paper is to derive the fractional Green’s function for the first time in the distributional space for the fractional-order integro-differential equation with constant coefficients. Our new technique is based on Babenko’s approach, without using any integral transforms such as the Laplace transform along with Mittag-Leffler function. The results obtained are not only much simpler, but also more generalized than the classical ones as they deal with distributions which are undefined in the ordinary sense in general. Furthermore, several interesting applications to solving the fractional differential and integral equations, as well as in the wave reaction-diffusion equation are provided, some of which cannot be achieved by integral transforms or numerical analysis. 2010 Mathematics Subject Classification. 46F10. 45J05, 26A33.
{"title":"The fractional Green's function by Babenko's approach","authors":"Chenkuan Li, Changpin Li","doi":"10.32513/tbilisi/1601344896","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344896","url":null,"abstract":"The goal of this paper is to derive the fractional Green’s function for the first time in the distributional space for the fractional-order integro-differential equation with constant coefficients. Our new technique is based on Babenko’s approach, without using any integral transforms such as the Laplace transform along with Mittag-Leffler function. The results obtained are not only much simpler, but also more generalized than the classical ones as they deal with distributions which are undefined in the ordinary sense in general. Furthermore, several interesting applications to solving the fractional differential and integral equations, as well as in the wave reaction-diffusion equation are provided, some of which cannot be achieved by integral transforms or numerical analysis. 2010 Mathematics Subject Classification. 46F10. 45J05, 26A33.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"19-42"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46057968","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344907
S. Olayemi, B. S. Ogundare
In this paper, existence of unique periodic solutions for two classes of third order delay differential equations are considered. The two equations are expressed in their integral equivalents with which suitable Green’s function is constructed and its associated properties stated. The main tool adopted to establish the existence of unique periodic solutions to the classes of delay differential equations is the Krasnoselskii’s fixed point theorem due to its applicability to the combination of a compact and contraction mappings which occur in dealing with perturbed differential operators.
{"title":"Periodic solutions to certain classes of third order delay differential equations","authors":"S. Olayemi, B. S. Ogundare","doi":"10.32513/tbilisi/1601344907","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344907","url":null,"abstract":"In this paper, existence of unique periodic solutions for two classes of third order delay differential equations are considered. The two equations are expressed in their integral equivalents with which suitable Green’s function is constructed and its associated properties stated. The main tool adopted to establish the existence of unique periodic solutions to the classes of delay differential equations is the Krasnoselskii’s fixed point theorem due to its applicability to the combination of a compact and contraction mappings which occur in dealing with perturbed differential operators.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"171-187"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42144196","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344897
Fariba Gharehgazlouei, S. Heidarkhani
{"title":"New existence criterion of infinitely many solutions for partial discrete Dirichlet problems","authors":"Fariba Gharehgazlouei, S. Heidarkhani","doi":"10.32513/tbilisi/1601344897","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344897","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"43-51"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41742508","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344903
Ali Khalouta, A. Kadem
{"title":"A new reliable method and its convergence for nonlinear second-order fractional differential equations","authors":"Ali Khalouta, A. Kadem","doi":"10.32513/tbilisi/1601344903","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344903","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"133-143"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43386539","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344899
A. Kashuri, M. Ali, M. Abbas, H. Budak, M. Sarıkaya
{"title":"Fractional integral inequalities for generalized convexity","authors":"A. Kashuri, M. Ali, M. Abbas, H. Budak, M. Sarıkaya","doi":"10.32513/tbilisi/1601344899","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344899","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"63-83"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49429896","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344894
S. S. Eker, Bilal Seker, S. Ece
{"title":"Coefficient bounds for subclasses of bi-univalent functions defined by fractional derivative operator","authors":"S. S. Eker, Bilal Seker, S. Ece","doi":"10.32513/tbilisi/1601344894","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344894","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"1-10"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45340762","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344901
A. K. Mishra, A. Prajapati, P. Gochhayat
{"title":"Third order differential subordination and superordination results for analytic functions involving the Hohlov operator","authors":"A. K. Mishra, A. Prajapati, P. Gochhayat","doi":"10.32513/tbilisi/1601344901","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344901","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"95-109"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47320002","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 : 2020-09-01DOI: 10.32513/tbilisi/1601344900
S. Kishor, P. Verma
{"title":"Some curvature properties on Lorentzian $beta$-Kenmotsu manifold with a semi-symmetric semi-metric connection","authors":"S. Kishor, P. Verma","doi":"10.32513/tbilisi/1601344900","DOIUrl":"https://doi.org/10.32513/tbilisi/1601344900","url":null,"abstract":"","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":"13 1","pages":"85-94"},"PeriodicalIF":0.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47320416","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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