Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity
In this paper, we will study solution existence and its stability for hybrid fractional DE with fractional integral, fractional differential derivative and Φp-operator in Caputo sense. Our problem deals with two basic types of fractional order derivatives, that is, Riemann-Liouville derivative of or...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2019.1663783 |
| _version_ | 1811338296318492672 |
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| author | Wadhah Al-Sadi Huang Zhenyou Abdulwasea Alkhazzan |
| author_facet | Wadhah Al-Sadi Huang Zhenyou Abdulwasea Alkhazzan |
| author_sort | Wadhah Al-Sadi |
| collection | DOAJ |
| description | In this paper, we will study solution existence and its stability for hybrid fractional DE with fractional integral, fractional differential derivative and Φp-operator in Caputo sense. Our problem deals with two basic types of fractional order derivatives, that is, Riemann-Liouville derivative of order $\delta $ and Caputo fractional derivative of order $\lambda , $ where $n - 1 \lt \lambda ,\sigma \le n, $ and $n \ge 3. $ We will transform the problem into an integral equation by using Green function and examine whether it is increasing or decreasing and positive or negative function. Some fixed point theorems (Krasnoselskii Theorem) are utilized for the existence of a positive solution (EPS). Addition to studying HU-stability technique for our suggested problem. An example is included to apply the results. |
| first_indexed | 2024-04-13T18:08:38Z |
| format | Article |
| id | doaj.art-00bbbcfd6b654a11966c007cfcc1209a |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-13T18:08:38Z |
| publishDate | 2019-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-00bbbcfd6b654a11966c007cfcc1209a2022-12-22T02:35:59ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552019-12-0113195196010.1080/16583655.2019.16637831663783Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularityWadhah Al-Sadi0Huang Zhenyou1Abdulwasea Alkhazzan2Nanjing University of Science and TechnologyNanjing University of Science and TechnologyHohai UniversityIn this paper, we will study solution existence and its stability for hybrid fractional DE with fractional integral, fractional differential derivative and Φp-operator in Caputo sense. Our problem deals with two basic types of fractional order derivatives, that is, Riemann-Liouville derivative of order $\delta $ and Caputo fractional derivative of order $\lambda , $ where $n - 1 \lt \lambda ,\sigma \le n, $ and $n \ge 3. $ We will transform the problem into an integral equation by using Green function and examine whether it is increasing or decreasing and positive or negative function. Some fixed point theorems (Krasnoselskii Theorem) are utilized for the existence of a positive solution (EPS). Addition to studying HU-stability technique for our suggested problem. An example is included to apply the results.http://dx.doi.org/10.1080/16583655.2019.1663783fractional derivativecaputo fractional derivativeriemann-liouvilleexistence of positive solutiongreen functionhyers-ulam stabilityhybrid fractional differential equation |
| spellingShingle | Wadhah Al-Sadi Huang Zhenyou Abdulwasea Alkhazzan Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity Journal of Taibah University for Science fractional derivative caputo fractional derivative riemann-liouville existence of positive solution green function hyers-ulam stability hybrid fractional differential equation |
| title | Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| title_full | Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| title_fullStr | Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| title_full_unstemmed | Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| title_short | Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| title_sort | existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity |
| topic | fractional derivative caputo fractional derivative riemann-liouville existence of positive solution green function hyers-ulam stability hybrid fractional differential equation |
| url | http://dx.doi.org/10.1080/16583655.2019.1663783 |
| work_keys_str_mv | AT wadhahalsadi existenceandstabilityofapositivesolutionfornonlinearhybridfractionaldifferentialequationswithsingularity AT huangzhenyou existenceandstabilityofapositivesolutionfornonlinearhybridfractionaldifferentialequationswithsingularity AT abdulwaseaalkhazzan existenceandstabilityofapositivesolutionfornonlinearhybridfractionaldifferentialequationswithsingularity |