The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/39699 |
| Acceso en línea: | https://hdl.handle.net/10347/39699 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Differential Equations Green’s Functions Boundary Value Problem 120215 Ecuaciones integrales |
| Sumario: | In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified Caputo fractional derivative of order α, CDβ is the Caputo fractional derivative of order β, and f is a function in C([0, 1] × R × R × R). Existence results for a solution are obtained. Two examples are presented to illustrate the results. |
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