Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses
| dc.contributor.author | Cao Labora, Daniel | |
| dc.contributor.author | Rodriguez-Lopez, Rosana | |
| dc.contributor.author | Belmekki, Mohammed | |
| dc.date.accessioned | 2021-09-21T15:12:34Z | |
| dc.date.available | 2021-09-21T15:12:34Z | |
| dc.date.issued | 2020-02-10 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Cao Labora, D., Rodríguez-López, R., & Belmekki, M. (2020). Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses. <i>Electronic Journal of Differential Equations, 2020</i>(15), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14519 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional differential equations | |
| dc.subject | Nonlocal boundary value problems | |
| dc.subject | Riemann-Liouville fractional derivative | |
| dc.subject | Fixed point results | |
| dc.title | Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses | |
| dc.type | Article |