Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3)
We study initial value problems of sequential fractional differential equations and inclusions involving a Caputo type differential operator of the form: $\left(^{C}D_{a+}^{\alpha }+\lambda _{1}~^{C}D_{a+}^{\alpha -1}+\lambda _{2}~^{C}D_{a+}^{\alpha -2}\right),$ where $\alpha \in (2,3)$ and $\lambda...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2017-09-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://www.etamaths.com/index.php/ijaa/article/view/1338 |
| _version_ | 1828961967745794048 |
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| author | Bashir Ahmad Mohammed M. Matar Ola M. El-Salmy |
| author_facet | Bashir Ahmad Mohammed M. Matar Ola M. El-Salmy |
| author_sort | Bashir Ahmad |
| collection | DOAJ |
| description | We study initial value problems of sequential fractional differential equations and inclusions involving a Caputo type differential operator of the form: $\left(^{C}D_{a+}^{\alpha }+\lambda _{1}~^{C}D_{a+}^{\alpha -1}+\lambda _{2}~^{C}D_{a+}^{\alpha -2}\right),$ where $\alpha \in (2,3)$ and $\lambda _{i} (i=1, 2) $ are nonzero constants. Several existence and uniqueness results are accomplished by means of fixed point theorems. Sufficient conditions for Ulam stability of the given problem are also presented. Examples are constructed for the illustration of obtained results. Then we investigate the inclusions case of the problem at hand. An initial value problem for coupled sequential fractional differential equations is also discussed. |
| first_indexed | 2024-12-14T09:56:38Z |
| format | Article |
| id | doaj.art-8af96c8bb769439cabe601debdb08f4d |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-14T09:56:38Z |
| publishDate | 2017-09-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-8af96c8bb769439cabe601debdb08f4d2022-12-21T23:07:23ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392017-09-0115186101264Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3)Bashir Ahmad0Mohammed M. Matar1Ola M. El-Salmy2King Abdulaziz UniversityAl-Azhar University-Gaza, PalestineAl-Azhar University-Gaza, PalestineWe study initial value problems of sequential fractional differential equations and inclusions involving a Caputo type differential operator of the form: $\left(^{C}D_{a+}^{\alpha }+\lambda _{1}~^{C}D_{a+}^{\alpha -1}+\lambda _{2}~^{C}D_{a+}^{\alpha -2}\right),$ where $\alpha \in (2,3)$ and $\lambda _{i} (i=1, 2) $ are nonzero constants. Several existence and uniqueness results are accomplished by means of fixed point theorems. Sufficient conditions for Ulam stability of the given problem are also presented. Examples are constructed for the illustration of obtained results. Then we investigate the inclusions case of the problem at hand. An initial value problem for coupled sequential fractional differential equations is also discussed.http://www.etamaths.com/index.php/ijaa/article/view/1338 |
| spellingShingle | Bashir Ahmad Mohammed M. Matar Ola M. El-Salmy Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) International Journal of Analysis and Applications |
| title | Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) |
| title_full | Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) |
| title_fullStr | Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) |
| title_full_unstemmed | Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) |
| title_short | Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3) |
| title_sort | existence of solutions and ulam stability for caputo type sequential fractional differential equations of order α ∈ 2 3 |
| url | http://www.etamaths.com/index.php/ijaa/article/view/1338 |
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