Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach
In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To ach...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/1/17 |
| _version_ | 1797493998773862400 |
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| author | Muhammad Yaseen Sadia Mumtaz Reny George Azhar Hussain |
| author_facet | Muhammad Yaseen Sadia Mumtaz Reny George Azhar Hussain |
| author_sort | Muhammad Yaseen |
| collection | DOAJ |
| description | In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings. |
| first_indexed | 2024-03-10T01:27:59Z |
| format | Article |
| id | doaj.art-a7c5e74c46274fee848451b4346814a6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:27:59Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-a7c5e74c46274fee848451b4346814a62023-11-23T13:48:41ZengMDPI AGFractal and Fractional2504-31102021-12-01611710.3390/fractalfract6010017Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s ApproachMuhammad Yaseen0Sadia Mumtaz1Reny George2Azhar Hussain3Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanIn this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.https://www.mdpi.com/2504-3110/6/1/17Caputo–Hadamard fractional derivativethermostat modelingCaputo–Hadamard fractional integralhybrid Caputo–Hadamard fractional differential equation and inclusion |
| spellingShingle | Muhammad Yaseen Sadia Mumtaz Reny George Azhar Hussain Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach Fractal and Fractional Caputo–Hadamard fractional derivative thermostat modeling Caputo–Hadamard fractional integral hybrid Caputo–Hadamard fractional differential equation and inclusion |
| title | Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach |
| title_full | Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach |
| title_fullStr | Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach |
| title_full_unstemmed | Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach |
| title_short | Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach |
| title_sort | existence results for the solution of the hybrid caputo hadamard fractional differential problems using dhage s approach |
| topic | Caputo–Hadamard fractional derivative thermostat modeling Caputo–Hadamard fractional integral hybrid Caputo–Hadamard fractional differential equation and inclusion |
| url | https://www.mdpi.com/2504-3110/6/1/17 |
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