On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative
In this paper, we presented and proved a general Lyapunov's inequality for a class of fractional boundary problems (FBPs) involving a new fractional derivative, named $ \lambda $-Hilfer. We proved a criterion of existence which extended that of Lyapunov concerning the ordinary case. We used thi...
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AIMS Press
2024-01-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024239?viewType=HTML |
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| author | Lakhdar Ragoub J. F. Gómez-Aguilar Eduardo Pérez-Careta Dumitru Baleanu |
| author_facet | Lakhdar Ragoub J. F. Gómez-Aguilar Eduardo Pérez-Careta Dumitru Baleanu |
| author_sort | Lakhdar Ragoub |
| collection | DOAJ |
| description | In this paper, we presented and proved a general Lyapunov's inequality for a class of fractional boundary problems (FBPs) involving a new fractional derivative, named $ \lambda $-Hilfer. We proved a criterion of existence which extended that of Lyapunov concerning the ordinary case. We used this criterion to solve the fractional differential equation (FDE) subject to the Dirichlet boundary conditions. In order to do so, we invoked some properties and essential results of $ \lambda $-Hilfer fractional boundary value problem (HFBVP). This result also retrieved all previous Lyapunov-type inequalities for different types of boundary conditions as mixed. The order that we considered here only focused on $ 1 < r\leq 2 $. General Hartman-Wintner-type inequalities were also investigated. We presented an example in order to provide an application of this result. |
| first_indexed | 2024-03-08T05:15:32Z |
| format | Article |
| id | doaj.art-dbfd03ce4784406eae7a825a84ce8df2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:15:32Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-dbfd03ce4784406eae7a825a84ce8df22024-02-07T01:19:55ZengAIMS PressAIMS Mathematics2473-69882024-01-01924907492410.3934/math.2024239On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivativeLakhdar Ragoub0J. F. Gómez-Aguilar1Eduardo Pérez-Careta2 Dumitru Baleanu31. Mathematics Department, Prince Muqrin University, Almadinah Almunawwarah, Saudi Arabia2. Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, Mexico3. Universidad de Guanajuato, Dpto. Electrónica, Carretera Salamanca-Valle de Santiago, Km 3+1.8, Salamanca Gto, México4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon 5. Institute of Space Sciences, Magurele-Bucharest, RomaniaIn this paper, we presented and proved a general Lyapunov's inequality for a class of fractional boundary problems (FBPs) involving a new fractional derivative, named $ \lambda $-Hilfer. We proved a criterion of existence which extended that of Lyapunov concerning the ordinary case. We used this criterion to solve the fractional differential equation (FDE) subject to the Dirichlet boundary conditions. In order to do so, we invoked some properties and essential results of $ \lambda $-Hilfer fractional boundary value problem (HFBVP). This result also retrieved all previous Lyapunov-type inequalities for different types of boundary conditions as mixed. The order that we considered here only focused on $ 1 < r\leq 2 $. General Hartman-Wintner-type inequalities were also investigated. We presented an example in order to provide an application of this result.https://www.aimspress.com/article/doi/10.3934/math.2024239?viewType=HTMLlyapunov's inequalityfractional integralgreen's functionhilfer hadamard integral |
| spellingShingle | Lakhdar Ragoub J. F. Gómez-Aguilar Eduardo Pérez-Careta Dumitru Baleanu On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative AIMS Mathematics lyapunov's inequality fractional integral green's function hilfer hadamard integral |
| title | On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative |
| title_full | On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative |
| title_fullStr | On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative |
| title_full_unstemmed | On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative |
| title_short | On a class of Lyapunov's inequality involving $ \lambda $-Hilfer Hadamard fractional derivative |
| title_sort | on a class of lyapunov s inequality involving lambda hilfer hadamard fractional derivative |
| topic | lyapunov's inequality fractional integral green's function hilfer hadamard integral |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024239?viewType=HTML |
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