Electron. J. Differential Equations,
Vol. 2020 (2020), No. 15, pp. 116.
Existence of solutions to nonlocal boundary value problems for fractional
differential equations with impulses
Daniel Cao Labora, Rosana RodriguezLopez, 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 ArzelaAscoli 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;
RiemannLiouville fractional derivative; fixed point results.
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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


Rosana RodríguezLópez
Departamento de Estadística, Análisis Matemático y Optimización
Universidade de Santiago de Compostela, 15782, Spain
email: rosana.rodriguez.lopez@usc.es


Mohammed Belmekki
Ecole Supérieure en Sciences Appliquées
BP. 165 RP, Bel Horizon
Tlemcen,13000, Algeria
email: m.belmekki@yahoo.fr

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