On abstract Hilfer fractional integrodifferential equations with boundary conditions
In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2020-08-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.03.001/full/pdf |
| _version_ | 1797791571835355136 |
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| author | Sabri T.M. Thabet Bashir Ahmad Ravi P. Agarwal |
| author_facet | Sabri T.M. Thabet Bashir Ahmad Ravi P. Agarwal |
| author_sort | Sabri T.M. Thabet |
| collection | DOAJ |
| description | In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions. |
| first_indexed | 2024-03-13T02:20:46Z |
| format | Article |
| id | doaj.art-2d17f3affdaf42aab351901959d9a69b |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:20:46Z |
| publishDate | 2020-08-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-2d17f3affdaf42aab351901959d9a69b2023-06-30T09:27:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142020-08-01261/210712510.1016/j.ajmsc.2019.03.001On abstract Hilfer fractional integrodifferential equations with boundary conditionsSabri T.M. Thabet0Bashir Ahmad1Ravi P. Agarwal2Department of Mathematics, University of Aden, Aden, YemenNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Texas A&M University, Kingsville, Texas, USAIn this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions.https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.03.001/full/pdfHilfer fractional integrodifferential equationsBoundary conditionsMönch fixed point theoremMeasure of noncompactnessExistenceContinuous dependence |
| spellingShingle | Sabri T.M. Thabet Bashir Ahmad Ravi P. Agarwal On abstract Hilfer fractional integrodifferential equations with boundary conditions Arab Journal of Mathematical Sciences Hilfer fractional integrodifferential equations Boundary conditions Mönch fixed point theorem Measure of noncompactness Existence Continuous dependence |
| title | On abstract Hilfer fractional integrodifferential equations with boundary conditions |
| title_full | On abstract Hilfer fractional integrodifferential equations with boundary conditions |
| title_fullStr | On abstract Hilfer fractional integrodifferential equations with boundary conditions |
| title_full_unstemmed | On abstract Hilfer fractional integrodifferential equations with boundary conditions |
| title_short | On abstract Hilfer fractional integrodifferential equations with boundary conditions |
| title_sort | on abstract hilfer fractional integrodifferential equations with boundary conditions |
| topic | Hilfer fractional integrodifferential equations Boundary conditions Mönch fixed point theorem Measure of noncompactness Existence Continuous dependence |
| url | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.03.001/full/pdf |
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