Lyapunov-type inequality for fractional BVPs involving two Hadamard fractional derivatives of different orders
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914526889246720 |
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| author | Laadjal, Zaid |
| author_facet | Laadjal, Zaid |
| contents | This paper establishes a Lyapunov-type inequality for a class of fractional boundary value problems (BVPs) involving two Hadamard fractional derivatives of different orders with Dirichlet boundary conditions. The method is based on the construction of the corresponding Green's function and establishing its maximum value through rigorous analytical techniques. The obtained inequality provides the necessary conditions for the existence of nontrivial solutions to the proposed problem. Finally, we illustrate the applicability of our results by establishing nonexistence criteria for nontrivial solutions to certain problems and providing examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov-type inequality for fractional BVPs involving two Hadamard fractional derivatives of different orders Laadjal, Zaid General Mathematics 26A33, 34A08, 26D10, 34B27 This paper establishes a Lyapunov-type inequality for a class of fractional boundary value problems (BVPs) involving two Hadamard fractional derivatives of different orders with Dirichlet boundary conditions. The method is based on the construction of the corresponding Green's function and establishing its maximum value through rigorous analytical techniques. The obtained inequality provides the necessary conditions for the existence of nontrivial solutions to the proposed problem. Finally, we illustrate the applicability of our results by establishing nonexistence criteria for nontrivial solutions to certain problems and providing examples. |
| title | Lyapunov-type inequality for fractional BVPs involving two Hadamard fractional derivatives of different orders |
| topic | General Mathematics 26A33, 34A08, 26D10, 34B27 |
| url | https://arxiv.org/abs/2602.13338 |