Some convergence results on proximal contractions with application to nonlinear fractional differential equation
In this manuscript, we investigated the coincidence points, best proximity points, and fixed-points results endowed with $ F $-contraction within the realm of suprametric spaces. The proximal point results obtained in this work show that our investigation is not purely theoretical; fundamental findi...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025247 |
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| author | Haroon Ahmad Om Prakash Chauhan Tania Angelica Lazăr Vasile Lucian Lazăr |
| author_facet | Haroon Ahmad Om Prakash Chauhan Tania Angelica Lazăr Vasile Lucian Lazăr |
| author_sort | Haroon Ahmad |
| collection | DOAJ |
| description | In this manuscript, we investigated the coincidence points, best proximity points, and fixed-points results endowed with $ F $-contraction within the realm of suprametric spaces. The proximal point results obtained in this work show that our investigation is not purely theoretical; fundamental findings were supplemented with concrete examples that demonstrate their practical ramifications. Furthermore, this paper focuses on boundary value problems (BVPs) related to nonlinear fractional differential equations of order $ 2 < \varpi \leq 3 $. By cleverly translating the BVP into an integral equation, we obtained conditions that confirm the existence and uniqueness of fixed points under $ (\mathscr{F}_{\tau })_{F_{\mathscr{P}}} $-contraction. A relevant part of this work is the approximation of the Green's function, which is critical in proving the existence and uniqueness of solutions. Our work not only adds to the current body of knowledge but also provides strong approaches for dealing with hard mathematical problems in the field of fractional differential equations. |
| format | Article |
| id | doaj-art-eca971f32aac4e93898679bf61e9f9af |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-eca971f32aac4e93898679bf61e9f9af2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-03-011035353537210.3934/math.2025247Some convergence results on proximal contractions with application to nonlinear fractional differential equationHaroon Ahmad0Om Prakash Chauhan1Tania Angelica Lazăr2Vasile Lucian Lazăr3Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan; Email: haroonrao3@gmail.comDepartment of Applied Mathematics, Jabalpur Engineering College, Jabalpur, India; Email: chauhaan.op@gmail.comDepartment of Mathematics, Technical University of Cluj Napoca, 400114 Cluj-Napoca, Romania; Email: tania.lazar@math.utcluj.roDepartment of Mathematics, Technical University of Cluj Napoca, 400114 Cluj-Napoca, Romania; Email: tania.lazar@math.utcluj.roIn this manuscript, we investigated the coincidence points, best proximity points, and fixed-points results endowed with $ F $-contraction within the realm of suprametric spaces. The proximal point results obtained in this work show that our investigation is not purely theoretical; fundamental findings were supplemented with concrete examples that demonstrate their practical ramifications. Furthermore, this paper focuses on boundary value problems (BVPs) related to nonlinear fractional differential equations of order $ 2 < \varpi \leq 3 $. By cleverly translating the BVP into an integral equation, we obtained conditions that confirm the existence and uniqueness of fixed points under $ (\mathscr{F}_{\tau })_{F_{\mathscr{P}}} $-contraction. A relevant part of this work is the approximation of the Green's function, which is critical in proving the existence and uniqueness of solutions. Our work not only adds to the current body of knowledge but also provides strong approaches for dealing with hard mathematical problems in the field of fractional differential equations.https://www.aimspress.com/article/doi/10.3934/math.2025247suprametric spacecoincidence pointbest proximity pointfixed pointgreen functionfractional boundary value problem |
| spellingShingle | Haroon Ahmad Om Prakash Chauhan Tania Angelica Lazăr Vasile Lucian Lazăr Some convergence results on proximal contractions with application to nonlinear fractional differential equation AIMS Mathematics suprametric space coincidence point best proximity point fixed point green function fractional boundary value problem |
| title | Some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| title_full | Some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| title_fullStr | Some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| title_full_unstemmed | Some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| title_short | Some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| title_sort | some convergence results on proximal contractions with application to nonlinear fractional differential equation |
| topic | suprametric space coincidence point best proximity point fixed point green function fractional boundary value problem |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025247 |
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