Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions
In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023059https://www.aimspress.com/article/doi/10.3934/math.2023059?viewType=HTML |
| _version_ | 1797989906146918400 |
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| author | Zaid Laadjal Fahd Jarad |
| author_facet | Zaid Laadjal Fahd Jarad |
| author_sort | Zaid Laadjal |
| collection | DOAJ |
| description | In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented. |
| first_indexed | 2024-04-11T08:28:04Z |
| format | Article |
| id | doaj.art-8fdbb72d2b0e43d1a26b78ab6f90dfa6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T08:28:04Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-8fdbb72d2b0e43d1a26b78ab6f90dfa62022-12-22T04:34:40ZengAIMS PressAIMS Mathematics2473-69882023-01-01811172119410.3934/math.2023059Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditionsZaid Laadjal0Fahd Jarad11. Department of Mathematics and Computer Science, University Center of Illizi, IIlizi, 33000, Algeria2. Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey 3. Department of Medical Research, China Medical University, Taichung 40402, TaiwanIn this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.https://www.aimspress.com/article/doi/10.3934/math.2023059https://www.aimspress.com/article/doi/10.3934/math.2023059?viewType=HTMLincomplete gamma functioncaputo-liouville proportional fractional derivativehybrid fractional integro-differential equationfixed point theoremulam-hyers stability |
| spellingShingle | Zaid Laadjal Fahd Jarad Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions AIMS Mathematics incomplete gamma function caputo-liouville proportional fractional derivative hybrid fractional integro-differential equation fixed point theorem ulam-hyers stability |
| title | Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions |
| title_full | Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions |
| title_fullStr | Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions |
| title_full_unstemmed | Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions |
| title_short | Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions |
| title_sort | existence uniqueness and stability of solutions for generalized proportional fractional hybrid integro differential equations with dirichlet boundary conditions |
| topic | incomplete gamma function caputo-liouville proportional fractional derivative hybrid fractional integro-differential equation fixed point theorem ulam-hyers stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023059https://www.aimspress.com/article/doi/10.3934/math.2023059?viewType=HTML |
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