On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative
In this paper, we investigate the existence and uniqueness of $ L^p $-solutions for nonlinear fractional differential and integro-differential equations with boundary conditions using the Caputo-Hadamard derivative. By employing Hölder's inequality together with the Krasnoselskii fixed-point th...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590366819221504 |
|---|---|
| author | Abduljawad Anwar Shayma Adil Murad |
| author_facet | Abduljawad Anwar Shayma Adil Murad |
| author_sort | Abduljawad Anwar |
| collection | DOAJ |
| description | In this paper, we investigate the existence and uniqueness of $ L^p $-solutions for nonlinear fractional differential and integro-differential equations with boundary conditions using the Caputo-Hadamard derivative. By employing Hölder's inequality together with the Krasnoselskii fixed-point theorem and the Banach contraction principle, the study establishes sufficient conditions for solving nonlinear problems. The paper delves into preliminary results, the existence and uniqueness of $ L^p $ solutions to the boundary value problem, and presents the Ulam-Hyers stability. Furthermore, it investigates the existence, uniqueness, and stability of solutions for fractional integro-differential equations. Through standard fixed-points and rigorous mathematical frameworks, this research contributes to the theoretical foundations of nonlinear fractional differential equations. Also, the Adomian decomposition method ($ {\mathcal{ADM}} $) is used to construct the analytical approximate solutions for the problems. Finally, examples are given that illustrate the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-f2e8715b30154068a0e5152b1c795162 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-f2e8715b30154068a0e5152b1c7951622025-01-24T01:02:16ZengAIMS PressMathematical Modelling and Control2767-89462024-12-014443945810.3934/mmc.2024035On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivativeAbduljawad Anwar0Shayma Adil Murad1Department of Mathematics, College of Science, University of Duhok, Duhok 42001, IraqDepartment of Mathematics, College of Science, University of Duhok, Duhok 42001, IraqIn this paper, we investigate the existence and uniqueness of $ L^p $-solutions for nonlinear fractional differential and integro-differential equations with boundary conditions using the Caputo-Hadamard derivative. By employing Hölder's inequality together with the Krasnoselskii fixed-point theorem and the Banach contraction principle, the study establishes sufficient conditions for solving nonlinear problems. The paper delves into preliminary results, the existence and uniqueness of $ L^p $ solutions to the boundary value problem, and presents the Ulam-Hyers stability. Furthermore, it investigates the existence, uniqueness, and stability of solutions for fractional integro-differential equations. Through standard fixed-points and rigorous mathematical frameworks, this research contributes to the theoretical foundations of nonlinear fractional differential equations. Also, the Adomian decomposition method ($ {\mathcal{ADM}} $) is used to construct the analytical approximate solutions for the problems. Finally, examples are given that illustrate the effectiveness of the theoretical results.https://www.aimspress.com/article/doi/10.3934/mmc.2024035fractional differential equations $ ({\mathcal{fde}}{s}) $caputo-hadamard ($ {\mathcal{ch}} $) derivativefixed-point theoremsulam-hyers $ ({\mathcal{uh}}) $ stabilityadomian decomposition method ($ {\mathcal{adm}} $) |
| spellingShingle | Abduljawad Anwar Shayma Adil Murad On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative Mathematical Modelling and Control fractional differential equations $ ({\mathcal{fde}}{s}) $ caputo-hadamard ($ {\mathcal{ch}} $) derivative fixed-point theorems ulam-hyers $ ({\mathcal{uh}}) $ stability adomian decomposition method ($ {\mathcal{adm}} $) |
| title | On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative |
| title_full | On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative |
| title_fullStr | On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative |
| title_full_unstemmed | On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative |
| title_short | On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative |
| title_sort | on the ulam stability and existence of l p solutions for fractional differential and integro differential equations with caputo hadamard derivative |
| topic | fractional differential equations $ ({\mathcal{fde}}{s}) $ caputo-hadamard ($ {\mathcal{ch}} $) derivative fixed-point theorems ulam-hyers $ ({\mathcal{uh}}) $ stability adomian decomposition method ($ {\mathcal{adm}} $) |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024035 |
| work_keys_str_mv | AT abduljawadanwar ontheulamstabilityandexistenceoflpsolutionsforfractionaldifferentialandintegrodifferentialequationswithcaputohadamardderivative AT shaymaadilmurad ontheulamstabilityandexistenceoflpsolutionsforfractionaldifferentialandintegrodifferentialequationswithcaputohadamardderivative |