RT Journal Article
T1 Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses
A1 Cao Labora, Daniel
A1 Rodríguez López, Rosana
A1 Belmekki, Mohammed
K1 Fractional differential equations
K1 Nonlocal boundary value problems
K1 Riemann-Liouville fractional derivative
K1 Fixed point results
AB 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.
PB Texas State University
SN 1072-6691
YR 2020
FD 2020-02-10
LK http://hdl.handle.net/10347/32759
UL http://hdl.handle.net/10347/32759
LA eng
NO Cao Labora, D., Rodríguez-López, R., Belmekki, M. (2020). Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses. “Electron. J. Differential Equations”, vol. 2020, no. 15, 1-16. DOI: 10.58997/ejde.2020.15
NO We are grateful for support by grant number MTM2016-75140-P (AEI/FEDER, UE), and by grant MTM2013-43014-P [Ministerio de Economía y Competitividad, co-financed by the European Community fund FEDER].
DS Minerva
RD 27 abr 2026