S-asymptotically omega-periodic mild solutions to fractional differential equations
| dc.contributor.author | Brindle, Darin | |
| dc.contributor.author | N'Guerekata, Gaston | |
| dc.date.accessioned | 2021-09-22T15:58:11Z | |
| dc.date.available | 2021-09-22T15:58:11Z | |
| dc.date.issued | 2020-04-07 | |
| dc.description.abstract | This article concerns the existence of mild solutions to the semi-linear fractional differential equation <pre>D<sup>α</sup><sub>t</sub>u(t) = Au(t) + D<sup>α-1</sup><sub>t</sub> ƒ(t, u(t)), t ≥ 0</pre> <p>with nonlocal conditions u(0) = u<sub>0</sub> + g(u) where D<sup>α</sup><sub>t</sub>(‧) (1 < α < 2) is the Riemann-Liouville derivative, A : D(A) ⊂ X → X is a linear densely defined operator of sectorial type on a complex Banach space X, ƒ : ℝ<sup>+</sup> x X → X is S-asymptotically ω-periodic with respect to the first variable. We use the Krsnoselskii's theorem to prove our main theorem. The results obtained are new even in the context of asymptotically ω-periodic functions. An application to fractional relaxation-oscillation equations is given. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Brindle, D., & N'Guérékata, G. M. (2020). S-asymptotically omega-periodic mild solutions to fractional differential equations. <i>Electronic Journal of Differential Equations, 2020</i>(30), pp. 1-12. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14534 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| 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 | S-asymptotically omega-periodic sequence | |
| dc.subject | Fractional semilinear differential equation | |
| dc.title | S-asymptotically omega-periodic mild solutions to fractional differential equations | |
| dc.type | Article |