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...

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Detalles Bibliográficos
Autores: Cao Labora, Daniel, Rodríguez López, Rosana, Belmekki, Mohammed
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
Descripción
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.