{"title":"Hopf-like bifurcation and mixed mode oscillation in a fractional-order FitzHugh-Nagumo model","authors":"Mohammed Salah Abdelouahab, R. Lozi","doi":"10.1063/1.5136214","DOIUrl":"https://doi.org/10.1063/1.5136214","url":null,"abstract":"In this work we investigate the emergence of mixed-mode oscillations and canard explosion, in a planar fractional-order FitzHugh-Nagumo model (FFHN). An algorithm, called Global-Local Canard Explosion Search Algorithm (GLCESA) is developed and used to investigate the existence of canard oscillations in the neighbourhoods of Hopf-like bifurcation points. the appearance of various patterns of solutions is revealed, with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied. The numbers of such oscillations versus the two parameters, respectively, are perfectly fitted using exponential functions. Finally, it is conjectured that chaos could occur in a 2-dimensional fractional-order autonomous dynamical system, with a fractional order close to one. After all, the article demonstrates that the FFHN Model is a very simple 2-dimensional model with an incredible ability to present the complex dynamics of neurons.","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129902152","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}
{"title":"On lacunary statistical convergence of order β of difference sequences of fractional order","authors":"N. D. Aral, M. Et","doi":"10.1063/1.5136140","DOIUrl":"https://doi.org/10.1063/1.5136140","url":null,"abstract":"The purpose of this paper is to introduce the concepts of Δα-lacunary statistical convergence of order β (0 < β ≤ 1) with the fractional order of α and Δα-lacunary strongly convergence of order β with the fractional order of α. We establish some connections between Δα-lacunary strongly convergence of order β and Δα-lacunary statistical convergence of order β.The purpose of this paper is to introduce the concepts of Δα-lacunary statistical convergence of order β (0 < β ≤ 1) with the fractional order of α and Δα-lacunary strongly convergence of order β with the fractional order of α. We establish some connections between Δα-lacunary strongly convergence of order β and Δα-lacunary statistical convergence of order β.","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128842753","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}
{"title":"Mathematical behaviour of solutions of the Kirchhoff type equation with logarithmic nonlinearity","authors":"E. Pişkin, Nazlı Irkıl","doi":"10.1063/1.5136208","DOIUrl":"https://doi.org/10.1063/1.5136208","url":null,"abstract":"In this work, we consider the Kirchhoff type equation with logarithmic nonlinearity. We obtain the global existence of the solutions by using the potential well method.","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132620515","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}
{"title":"On the exponentiated Weibull distribution","authors":"N. Al-Noor, S. Abid, M. A. A. Boshi","doi":"10.1063/1.5136220","DOIUrl":"https://doi.org/10.1063/1.5136220","url":null,"abstract":"","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128751344","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}
{"title":"A new extension on absolute matrix summability factors of infinite series","authors":"Ş. Yıldız","doi":"10.1063/1.5136154","DOIUrl":"https://doi.org/10.1063/1.5136154","url":null,"abstract":"","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116487129","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}
{"title":"On the numerical analysis of a nonlinear fractional Schrödinger equation with Neumann boundary condition","authors":"B. Hicdurmaz","doi":"10.1063/1.5136184","DOIUrl":"https://doi.org/10.1063/1.5136184","url":null,"abstract":"","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"375 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123494611","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}
{"title":"On m* − g−closed sets and m* − R0 spaces in a hereditary m−space (X, m, H)","authors":"T. Noiri, A. Acikgoz","doi":"10.1063/1.5136117","DOIUrl":"https://doi.org/10.1063/1.5136117","url":null,"abstract":"","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121785154","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}
{"title":"Pseudo almost periodic generalized functions","authors":"M. T. Khalladi","doi":"10.1063/1.5136134","DOIUrl":"https://doi.org/10.1063/1.5136134","url":null,"abstract":"","PeriodicalId":175596,"journal":{"name":"THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019)","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121576195","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}