On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions
This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle of the Banach and Leray–Schauder fixed point theore...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/1/13 |
| _version_ | 1797442297218990080 |
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| author | Limin Guo Usman Riaz Akbar Zada Mehboob Alam |
| author_facet | Limin Guo Usman Riaz Akbar Zada Mehboob Alam |
| author_sort | Limin Guo |
| collection | DOAJ |
| description | This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle of the Banach and Leray–Schauder fixed point theorems. Moreover, with two different approaches, the Hyers–Ulam stabilities are also discussed. Different ordinary differential equations of the third order with different boundary conditions (e.g., initial, anti periodic and integro-differential) can be obtained as a special case for our proposed model. Finally, for verification, an example is presented, and some graphs for the particular variables and particular functions are drawn using MATLAB. |
| first_indexed | 2024-03-09T12:40:48Z |
| format | Article |
| id | doaj.art-581762d26a754f038a4c9cbef5b5c42c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T12:40:48Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-581762d26a754f038a4c9cbef5b5c42c2023-11-30T22:18:57ZengMDPI AGFractal and Fractional2504-31102022-12-01711310.3390/fractalfract7010013On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary ConditionsLimin Guo0Usman Riaz1Akbar Zada2Mehboob Alam3School of Science, Changzhou Institute of Technology, Changzhou 213002, ChinaDepartment of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology, Peshawar 29050, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25120, PakistanFaculty of Engineering Science, Ghulam Ishaq Khan Institute of Engineering Science and Technology, Topi 23640, PakistanThis study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle of the Banach and Leray–Schauder fixed point theorems. Moreover, with two different approaches, the Hyers–Ulam stabilities are also discussed. Different ordinary differential equations of the third order with different boundary conditions (e.g., initial, anti periodic and integro-differential) can be obtained as a special case for our proposed model. Finally, for verification, an example is presented, and some graphs for the particular variables and particular functions are drawn using MATLAB.https://www.mdpi.com/2504-3110/7/1/13Hadamard fractional derivativecoupled systemsboundary value problemexistence of solutionsUlam stability |
| spellingShingle | Limin Guo Usman Riaz Akbar Zada Mehboob Alam On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions Fractal and Fractional Hadamard fractional derivative coupled systems boundary value problem existence of solutions Ulam stability |
| title | On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions |
| title_full | On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions |
| title_fullStr | On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions |
| title_full_unstemmed | On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions |
| title_short | On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions |
| title_sort | on implicit coupled hadamard fractional differential equations with generalized hadamard fractional integro differential boundary conditions |
| topic | Hadamard fractional derivative coupled systems boundary value problem existence of solutions Ulam stability |
| url | https://www.mdpi.com/2504-3110/7/1/13 |
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