Delay dynamic double integral inequalities on time scales with applications
Abstract In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As applications, the boundedness for the solutions of delay dynamic integro-differenti...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-2516-3 |
| _version_ | 1828891455616188416 |
|---|---|
| author | Sobia Rafeeq Humaira Kalsoom Sabir Hussain Saima Rashid Yu-Ming Chu |
| author_facet | Sobia Rafeeq Humaira Kalsoom Sabir Hussain Saima Rashid Yu-Ming Chu |
| author_sort | Sobia Rafeeq |
| collection | DOAJ |
| description | Abstract In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As applications, the boundedness for the solutions of delay dynamic integro-differential equations with initial conditions is discussed. |
| first_indexed | 2024-12-13T13:17:22Z |
| format | Article |
| id | doaj.art-841895d1d8004f5d887d72a516a46284 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T13:17:22Z |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-841895d1d8004f5d887d72a516a462842022-12-21T23:44:29ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020113210.1186/s13662-020-2516-3Delay dynamic double integral inequalities on time scales with applicationsSobia Rafeeq0Humaira Kalsoom1Sabir Hussain2Saima Rashid3Yu-Ming Chu4Department of Mathematics and Statistics, University of LahoreSchool of Mathematical Sciences, Zhejiang UniversityDepartment of Mathematics, University of Engineering and TechnologyDepartment of Mathematics, Government College (GC) UniversityDepartment of Mathematics, Huzhou UniversityAbstract In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As applications, the boundedness for the solutions of delay dynamic integro-differential equations with initial conditions is discussed.https://doi.org/10.1186/s13662-020-2516-3Delay integral inequalityTime scaleDynamic equationDiscrete inequalityBoundedness |
| spellingShingle | Sobia Rafeeq Humaira Kalsoom Sabir Hussain Saima Rashid Yu-Ming Chu Delay dynamic double integral inequalities on time scales with applications Advances in Difference Equations Delay integral inequality Time scale Dynamic equation Discrete inequality Boundedness |
| title | Delay dynamic double integral inequalities on time scales with applications |
| title_full | Delay dynamic double integral inequalities on time scales with applications |
| title_fullStr | Delay dynamic double integral inequalities on time scales with applications |
| title_full_unstemmed | Delay dynamic double integral inequalities on time scales with applications |
| title_short | Delay dynamic double integral inequalities on time scales with applications |
| title_sort | delay dynamic double integral inequalities on time scales with applications |
| topic | Delay integral inequality Time scale Dynamic equation Discrete inequality Boundedness |
| url | https://doi.org/10.1186/s13662-020-2516-3 |
| work_keys_str_mv | AT sobiarafeeq delaydynamicdoubleintegralinequalitiesontimescaleswithapplications AT humairakalsoom delaydynamicdoubleintegralinequalitiesontimescaleswithapplications AT sabirhussain delaydynamicdoubleintegralinequalitiesontimescaleswithapplications AT saimarashid delaydynamicdoubleintegralinequalitiesontimescaleswithapplications AT yumingchu delaydynamicdoubleintegralinequalitiesontimescaleswithapplications |