A New Gronwall-Bellman Inequality in Frame of Generalized Proportional Fractional Derivative
| dc.contributor.author | Alzabut, Jehad | |
| dc.contributor.author | Sudsutad, Weerawat | |
| dc.contributor.author | Kayar, Zeynep | |
| dc.contributor.author | Baghani, Hamid | |
| dc.date.accessioned | 2025-05-10T17:25:42Z | |
| dc.date.available | 2025-05-10T17:25:42Z | |
| dc.date.issued | 2019 | |
| dc.description | Sudsutad, Weerawat/0000-0002-6762-813X; Baghani, Mostafa/0000-0001-6695-3128; Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138 | en_US |
| dc.description.abstract | New versions of a Gronwall-Bellman inequality in the frame of the generalized (Riemann-Liouville and Caputo) proportional fractional derivative are provided. Before proceeding to the main results, we define the generalized Riemann-Liouville and Caputo proportional fractional derivatives and integrals and expose some of their features. We prove our main result in light of some efficient comparison analyses. The Gronwall-Bellman inequality in the case of weighted function is also obtained. By the help of the new proposed inequalities, examples of Riemann-Liouville and Caputo proportional fractional initial value problems are presented to emphasize the solution dependence on the initial data and on the right-hand side. | en_US |
| dc.description.sponsorship | Prince Sultan University [RG-DES-2017-01-17] | en_US |
| dc.description.sponsorship | The first author would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17. | en_US |
| dc.identifier.doi | 10.3390/math7080747 | |
| dc.identifier.issn | 2227-7390 | |
| dc.identifier.scopus | 2-s2.0-85071179055 | |
| dc.identifier.uri | https://doi.org/10.3390/math7080747 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14720/11443 | |
| dc.language.iso | en | en_US |
| dc.publisher | Mdpi | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Gronwall-Bellman Inequality | en_US |
| dc.subject | Proportional Fractional Derivative | en_US |
| dc.subject | Riemann-Liouville And Caputo Proportional Fractional Initial Value Problem | en_US |
| dc.title | A New Gronwall-Bellman Inequality in Frame of Generalized Proportional Fractional Derivative | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.id | Sudsutad, Weerawat/0000-0002-6762-813X | |
| gdc.author.id | Baghani, Mostafa/0000-0001-6695-3128 | |
| gdc.author.id | Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138 | |
| gdc.author.scopusid | 13105947900 | |
| gdc.author.scopusid | 54950180800 | |
| gdc.author.scopusid | 55695817800 | |
| gdc.author.scopusid | 43461211600 | |
| gdc.author.wosid | Baghani, Mostafa/U-2864-2018 | |
| gdc.author.wosid | Alzabut, Prof. Dr. Jehad/T-8075-2018 | |
| gdc.coar.access | open access | |
| gdc.coar.type | text::journal::journal article | |
| gdc.description.department | T.C. Van Yüzüncü Yıl Üniversitesi | en_US |
| gdc.description.departmenttemp | [Alzabut, Jehad] Prince Sultan, Dept Math & Gen Sci, POB 66833, Riyadh 11586, Saudi Arabia; [Sudsutad, Weerawat] Navamindradhiraj Univ, Fac Sci & Hlth Technol, Dept Gen Educ, Bangkok 10300, Thailand; [Kayar, Zeynep] Van Yuzuncu Yil Univ, Dept Math, TR-65080 Van, Turkey; [Baghani, Hamid] Univ Sistan & Baluchestan, Fac Math, Dept Math, Zahedan, Iran | en_US |
| gdc.description.issue | 8 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q2 | |
| gdc.description.volume | 7 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
| gdc.description.wosquality | Q1 | |
| gdc.identifier.wos | WOS:000482856500069 | |
| gdc.index.type | WoS | |
| gdc.index.type | Scopus |