Pub Date : 2019-07-01DOI: 10.1016/j.ajmsc.2019.05.003
M. Kamarujjama, N.U. Khan, Owais Khan
In this paper, we establish fractional integral and derivative formulas involving the generalized p-k-Mittag-Leffler function by using Marichev–Saigo–Maeda type fractional integral and derivative operators. We also consider some special cases of derived results by considering specific values of the parameters of the generalized p-k-Mittag-Leffler function to give the application of our main results.
{"title":"Fractional calculus of generalized p-k-Mittag-Leffler function using Marichev–Saigo–Maeda operators","authors":"M. Kamarujjama, N.U. Khan, Owais Khan","doi":"10.1016/j.ajmsc.2019.05.003","DOIUrl":"10.1016/j.ajmsc.2019.05.003","url":null,"abstract":"<div><p>In this paper, we establish fractional integral and derivative formulas involving the generalized p-k-Mittag-Leffler function by using Marichev–Saigo–Maeda type fractional integral and derivative operators. We also consider some special cases of derived results by considering specific values of the parameters of the generalized p-k-Mittag-Leffler function to give the application of our main results.</p></div>","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"25 2","pages":"Pages 156-168"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ajmsc.2019.05.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45754092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-22DOI: 10.1016/J.AJMSC.2019.05.002
Adrian Magdaș
{"title":"Coupled fixed points and coupled best proximity points for cyclic Ćirić type operators","authors":"Adrian Magdaș","doi":"10.1016/J.AJMSC.2019.05.002","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.05.002","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.05.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47349703","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 : 2019-04-20DOI: 10.1016/J.AJMSC.2019.04.001
Dongming Wei, S. Al-Ashhab
{"title":"Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids","authors":"Dongming Wei, S. Al-Ashhab","doi":"10.1016/J.AJMSC.2019.04.001","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.04.001","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.04.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45128647","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 : 2019-03-25DOI: 10.1016/j.ajmsc.2019.09.001
E. Ballico
{"title":"Reconstruction of a homogeneous polynomial from its additive decompositions when identifiability fails","authors":"E. Ballico","doi":"10.1016/j.ajmsc.2019.09.001","DOIUrl":"https://doi.org/10.1016/j.ajmsc.2019.09.001","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ajmsc.2019.09.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49017461","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 : 2019-03-15DOI: 10.1016/J.AJMSC.2019.03.002
T. Saanouni
{"title":"Remarks on the critical nonlinear high-order heat equation","authors":"T. Saanouni","doi":"10.1016/J.AJMSC.2019.03.002","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.03.002","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43146192","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 : 2019-03-14DOI: 10.1016/J.AJMSC.2019.03.001
S. T. Thabet, B. Ahmad, R. Agarwal
{"title":"On abstract Hilfer fractional integrodifferential equations with boundary conditions","authors":"S. T. Thabet, B. Ahmad, R. Agarwal","doi":"10.1016/J.AJMSC.2019.03.001","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.03.001","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43015694","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 : 2019-02-08DOI: 10.1016/J.AJMSC.2019.02.001
G. A. Okeke, S. H. Khan
{"title":"Approximation of fixed point of multivalued ρ-quasi-contractive mappings in modular function spaces","authors":"G. A. Okeke, S. H. Khan","doi":"10.1016/J.AJMSC.2019.02.001","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.02.001","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.02.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45996527","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 : 2019-01-07DOI: 10.1108/ajms-01-2021-0015
Gh. Fasihi-Ramandi, S. Azami
PurposeIn this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.Design/methodology/approachIn the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H2n+1 have constant negative scalar curvature.FindingsIn the second part, we present our main results. We show that the Heisenberg group H2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.Originality/valueIn this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.
{"title":"Geometry of left-invariant Randers metric on the Heisenberg groups","authors":"Gh. Fasihi-Ramandi, S. Azami","doi":"10.1108/ajms-01-2021-0015","DOIUrl":"https://doi.org/10.1108/ajms-01-2021-0015","url":null,"abstract":"PurposeIn this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.Design/methodology/approachIn the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H2n+1 have constant negative scalar curvature.FindingsIn the second part, we present our main results. We show that the Heisenberg group H2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.Originality/valueIn this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46917100","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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