Daniel Cao Labora, Rosana Rodriguez-Lopez, Mohammed Belmekki
Abstract:
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 Arzela-Ascoli theorem
that makes it suitable for piecewise uniformly continuous functions.
Submitted May 9, 2018. Published February 10, 2020.
Math Subject Classifications: 26A33, 34B37, 34B05, 34B10, 34B27.
Key Words: Fractional differential equations; nonlocal boundary value problems;
Riemann-Liouville fractional derivative; fixed point results.
DOI: 10.58997/ejde.2020.15
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Daniel Cao Labora Departamento de Estadística, Análisis Matemático y Optimización Universidade de Santiago de Compostela, 15782, Spain email: daniel.cao@usc.es |
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Rosana Rodríguez-López Departamento de Estadística, Análisis Matemático y Optimización Universidade de Santiago de Compostela, 15782, Spain email: rosana.rodriguez.lopez@usc.es |
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Mohammed Belmekki Ecole Supérieure en Sciences Appliquées BP. 165 RP, Bel Horizon Tlemcen,13000, Algeria email: m.belmekki@yahoo.fr |
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