Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs
Abstract In this paper, we study some new Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as effective tools i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-2504-7 |
| _version_ | 1818611847901741056 |
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| author | Haidong Liu Chuancun Yin |
| author_facet | Haidong Liu Chuancun Yin |
| author_sort | Haidong Liu |
| collection | DOAJ |
| description | Abstract In this paper, we study some new Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as effective tools in the qualitative theory of certain classes of partial dynamic equations on time scales. Finally, an example is provided to illustrate the usefulness of our result. |
| first_indexed | 2024-12-16T15:36:50Z |
| format | Article |
| id | doaj.art-ed6efbb6ecf6461db18fd034f988f6e7 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T15:36:50Z |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-ed6efbb6ecf6461db18fd034f988f6e72022-12-21T22:26:10ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020112010.1186/s13662-020-2504-7Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairsHaidong Liu0Chuancun Yin1School of Mathematical Sciences, Qufu Normal UniversitySchool of Statistics, Qufu Normal UniversityAbstract In this paper, we study some new Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as effective tools in the qualitative theory of certain classes of partial dynamic equations on time scales. Finally, an example is provided to illustrate the usefulness of our result.https://doi.org/10.1186/s13662-020-2504-7Time scaleDynamical integral inequalityVolterra–Fredholm typeTwo independent variables |
| spellingShingle | Haidong Liu Chuancun Yin Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs Advances in Difference Equations Time scale Dynamical integral inequality Volterra–Fredholm type Two independent variables |
| title | Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| title_full | Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| title_fullStr | Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| title_full_unstemmed | Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| title_short | Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| title_sort | some generalized volterra fredholm type dynamical integral inequalities in two independent variables on time scale pairs |
| topic | Time scale Dynamical integral inequality Volterra–Fredholm type Two independent variables |
| url | https://doi.org/10.1186/s13662-020-2504-7 |
| work_keys_str_mv | AT haidongliu somegeneralizedvolterrafredholmtypedynamicalintegralinequalitiesintwoindependentvariablesontimescalepairs AT chuancunyin somegeneralizedvolterrafredholmtypedynamicalintegralinequalitiesintwoindependentvariablesontimescalepairs |