A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems
| dc.contributor.author | Webb, Jeffrey | |
| dc.date.accessioned | 2022-10-25T19:08:55Z | |
| dc.date.available | 2022-10-25T19:08:55Z | |
| dc.date.issued | 2021-09-20 | |
| dc.description.abstract | We study the asymptotic behaviour of global solutions of some nonlinear integral equations related to some Caputo fractional initial value problems. We consider problems of fractional order between 0 and 1 and of order between 1 and 2, each in two cases: when the nonlinearity depends only on the function, and when the nonlinearity also depends on fractional derivatives of lower order. Our main tool is a new Gronwall inequality for integrals with singular kernels, which we prove here, and a related boundedness property of a fractional integral of an L1[0, ∞) function. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Webb, J. R. L. (2021). A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems. <i>Electronic Journal of Differential Equations, 2021</i>(80), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16238 | |
| 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, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional derivatives | |
| dc.subject | Asymptotic behaviour | |
| dc.subject | Gronwall inequality | |
| dc.subject | Weakly singular kernel | |
| dc.title | A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems | |
| dc.type | Article |