On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay
We give a representation of solutions to linear nonhomogeneous Ψ-fractional delayed differential equations with noncommutative matrices. We newly define Ψ-delay perturbation of Mittag-Leffler type matrix function with two parameters and apply the method of variation of constants to obtain the repres...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022053?viewType=HTML |
| _version_ | 1811250917414010880 |
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| author | Mustafa Aydin Nazim I. Mahmudov Hüseyin Aktuğlu Erdem Baytunç Mehmet S. Atamert |
| author_facet | Mustafa Aydin Nazim I. Mahmudov Hüseyin Aktuğlu Erdem Baytunç Mehmet S. Atamert |
| author_sort | Mustafa Aydin |
| collection | DOAJ |
| description | We give a representation of solutions to linear nonhomogeneous Ψ-fractional delayed differential equations with noncommutative matrices. We newly define Ψ-delay perturbation of Mittag-Leffler type matrix function with two parameters and apply the method of variation of constants to obtain the representation of the solutions. We investigate the existence and uniqueness of solutions for a class of Ψ-fractional delayed semilinear differential equations by using Banach Fixed Point Theorem. Further, we establish the Ulam-Hyers stability result for the analyzed problem. Finally, we provide some examples to illustrate the applicability of our results. |
| first_indexed | 2024-04-12T16:11:56Z |
| format | Article |
| id | doaj.art-7f596b265cc14e39a774515e5b52a2f5 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T16:11:56Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-7f596b265cc14e39a774515e5b52a2f52022-12-22T03:25:52ZengAIMS PressElectronic Research Archive2688-15942022-03-013031016103410.3934/era.2022053On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delayMustafa Aydin0Nazim I. Mahmudov1Hüseyin Aktuğlu2 Erdem Baytunç 3Mehmet S. Atamert41. Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Mersin 10, Turkey 2. Department of Mathematics, Istanbul Technical University, Sariyer, Istanbul 34469, Turkey1. Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Mersin 10, Turkey1. Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Mersin 10, Turkey1. Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Mersin 10, Turkey1. Department of Mathematics, Eastern Mediterranean University, Famagusta 99628 T.R. North Cyprus, Mersin 10, TurkeyWe give a representation of solutions to linear nonhomogeneous Ψ-fractional delayed differential equations with noncommutative matrices. We newly define Ψ-delay perturbation of Mittag-Leffler type matrix function with two parameters and apply the method of variation of constants to obtain the representation of the solutions. We investigate the existence and uniqueness of solutions for a class of Ψ-fractional delayed semilinear differential equations by using Banach Fixed Point Theorem. Further, we establish the Ulam-Hyers stability result for the analyzed problem. Finally, we provide some examples to illustrate the applicability of our results.https://www.aimspress.com/article/doi/10.3934/era.2022053?viewType=HTMLmittag-leffler type matrix functionfractional linear and nonlinear systemsψ-caputo derivative representation of solutionsdelayed perturbation |
| spellingShingle | Mustafa Aydin Nazim I. Mahmudov Hüseyin Aktuğlu Erdem Baytunç Mehmet S. Atamert On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay Electronic Research Archive mittag-leffler type matrix function fractional linear and nonlinear systems ψ-caputo derivative representation of solutions delayed perturbation |
| title | On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay |
| title_full | On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay |
| title_fullStr | On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay |
| title_full_unstemmed | On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay |
| title_short | On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay |
| title_sort | on a study of the representation of solutions of a ψ caputo fractional differential equations with a single delay |
| topic | mittag-leffler type matrix function fractional linear and nonlinear systems ψ-caputo derivative representation of solutions delayed perturbation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022053?viewType=HTML |
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