Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator
In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s tech...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9993177 |
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| author | Abdellatif Boutiara Mohammed M. Matar Mohammed K. A. Kaabar Francisco Martínez Sina Etemad Shahram Rezapour |
| author_facet | Abdellatif Boutiara Mohammed M. Matar Mohammed K. A. Kaabar Francisco Martínez Sina Etemad Shahram Rezapour |
| author_sort | Abdellatif Boutiara |
| collection | DOAJ |
| description | In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results. |
| format | Article |
| id | doaj-art-137a63de0b334c6b94ce0b23cc399159 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-137a63de0b334c6b94ce0b23cc3991592025-02-03T07:24:25ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99931779993177Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo OperatorAbdellatif Boutiara0Mohammed M. Matar1Mohammed K. A. Kaabar2Francisco Martínez3Sina Etemad4Shahram Rezapour5Laboratory of Mathematics and Applied Sciences, University of Ghardaia, 47000, AlgeriaDepartment of Mathematics, Al-Azhar University-Gaza, Gaza Strip, State of PalestineJabalia Camp, United Nations Relief and Works Agency (UNRWA) Palestinian Refugee Camp, Gaza Strip Jabalya, State of PalestineDepartment of Applied Mathematics and Statistics, Technological University of Cartagena, Cartagena 30203, SpainDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranIn this paper, a new class of a neutral functional delay differential equation involving the generalized ψ-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.http://dx.doi.org/10.1155/2021/9993177 |
| spellingShingle | Abdellatif Boutiara Mohammed M. Matar Mohammed K. A. Kaabar Francisco Martínez Sina Etemad Shahram Rezapour Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator Journal of Function Spaces |
| title | Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator |
| title_full | Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator |
| title_fullStr | Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator |
| title_full_unstemmed | Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator |
| title_short | Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator |
| title_sort | some qualitative analyses of neutral functional delay differential equation with generalized caputo operator |
| url | http://dx.doi.org/10.1155/2021/9993177 |
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