Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses
In this work, through the application of fixed point theory, we consider the properties of the solutions to a nonlocal boundary value problem for fractional differential equations subject to impulses at fixed times. We compute the Green's function related to the problem, which allows us to obta...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:10347/32759 |
| Acceso en línea: | http://hdl.handle.net/10347/32759 |
| Access Level: | acceso abierto |
| Palabra clave: | 1202.19 Ecuaciones Diferenciales Ordinarias |
| Sumario: | In this work, through the application of fixed point theory, we consider the properties of the solutions to a nonlocal boundary value problem for fractional differential equations subject to impulses at fixed times. We compute the Green's function related to the problem, which allows us to obtain an integral representation of the solution. This representation gives an explicit description of the solution when the source term does not depend on the solution. Nevertheless, when the description of the source term is implicit, we can not ensure the existence of a solution. In this case, we prove the existence of a solution for the integral problem via fixed point techniques. To do this, we develop a slight generalization of Arzelà-Ascoli theorem that makes it suitable for piecewise uniformly continuous functions. |
|---|