On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation
In this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2015-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X14001308 |
| _version_ | 1818278738786254848 |
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| author | A. Abdeldaim A.A. El-Deeb |
| author_facet | A. Abdeldaim A.A. El-Deeb |
| author_sort | A. Abdeldaim |
| collection | DOAJ |
| description | In this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions. |
| first_indexed | 2024-12-12T23:22:13Z |
| format | Article |
| id | doaj.art-a1eeab21b73d40aa889fb90f84225849 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T23:22:13Z |
| publishDate | 2015-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-a1eeab21b73d40aa889fb90f842258492022-12-22T00:08:15ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2015-10-0123347047510.1016/j.joems.2014.12.001On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equationA. Abdeldaim0A.A. El-Deeb1Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, EgyptDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, EgyptIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions.http://www.sciencedirect.com/science/article/pii/S1110256X14001308Integral inequalityAnalysis techniqueEstimationRetarded integral and differential equation |
| spellingShingle | A. Abdeldaim A.A. El-Deeb On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation Journal of the Egyptian Mathematical Society Integral inequality Analysis technique Estimation Retarded integral and differential equation |
| title | On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| title_full | On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| title_fullStr | On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| title_full_unstemmed | On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| title_short | On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| title_sort | on some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation |
| topic | Integral inequality Analysis technique Estimation Retarded integral and differential equation |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X14001308 |
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