On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications
Abstract This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. The continuous dependence of the solution on the set of selections of the set-valued function will be proven. As an application, we study the existence...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-2531-4 |
| _version_ | 1818920278933110784 |
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| author | Ahmed Mohamed El-Sayed Shorouk Mahmoud Al-Issa |
| author_facet | Ahmed Mohamed El-Sayed Shorouk Mahmoud Al-Issa |
| author_sort | Ahmed Mohamed El-Sayed |
| collection | DOAJ |
| description | Abstract This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. The continuous dependence of the solution on the set of selections of the set-valued function will be proven. As an application, we study the existence of solutions to an initial-value problem of arbitrary fractional-order differential inclusion. |
| first_indexed | 2024-12-20T01:19:13Z |
| format | Article |
| id | doaj.art-cc950e4c6d3242c68e206d043917167e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-20T01:19:13Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-cc950e4c6d3242c68e206d043917167e2022-12-21T19:58:29ZengSpringerOpenAdvances in Difference Equations1687-18472020-02-012020111610.1186/s13662-020-2531-4On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applicationsAhmed Mohamed El-Sayed0Shorouk Mahmoud Al-Issa1Faculty of Science, Alexandria UniversityDepartment of Mathematics, Lebanese International UniversityAbstract This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. The continuous dependence of the solution on the set of selections of the set-valued function will be proven. As an application, we study the existence of solutions to an initial-value problem of arbitrary fractional-order differential inclusion.https://doi.org/10.1186/s13662-020-2531-4Nonlinear Volterra–Stieltjes integral equationFunctional integral inclusionFunction of bounded variationMaximal and minimal solutions |
| spellingShingle | Ahmed Mohamed El-Sayed Shorouk Mahmoud Al-Issa On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications Advances in Difference Equations Nonlinear Volterra–Stieltjes integral equation Functional integral inclusion Function of bounded variation Maximal and minimal solutions |
| title | On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications |
| title_full | On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications |
| title_fullStr | On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications |
| title_full_unstemmed | On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications |
| title_short | On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications |
| title_sort | on the existence of solutions of a set valued functional integral equation of volterra stieltjes type and some applications |
| topic | Nonlinear Volterra–Stieltjes integral equation Functional integral inclusion Function of bounded variation Maximal and minimal solutions |
| url | https://doi.org/10.1186/s13662-020-2531-4 |
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