Initial value problems for Caputo fractional equations with singular nonlinearities
| dc.contributor.author | Webb, Jeffrey | |
| dc.date.accessioned | 2021-12-06T16:00:24Z | |
| dc.date.available | 2021-12-06T16:00:24Z | |
| dc.date.issued | 2019-10-30 | |
| dc.description.abstract | We consider initial value problems for Caputo fractional equations of the form DαCu = ƒ where ƒ can have a singularity. We consider all orders and prove equivalences with Volterra integral equations in classical spaces such as Cm [0, T]. In particular for the case 1 < α < 2 we consider nonlinearities of the form t-γ ƒ(t, u, DβCu) where 0 < β ≤ 1 and 0 ≤ γ < 1 with ƒ continuous, and we prove results on existence of global C1 solutions under linear growth assumptions on ƒ(t, u, p) in the u, p variables. With a Lipschitz condition we prove continuous dependence on the initial data and uniqueness. One tool we use is a Gronwall inequality for weakly singular problems with double singularities. We also prove some regularity results and discuss monotonicity and concavity properties. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 34 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Webb, J. R. L. (2019). Initial value problems for Caputo fractional equations with singular nonlinearities. <i>Electronic Journal of Differential Equations, 2019</i>(117), pp. 1-32. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15011 | |
| 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, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional derivatives | |
| dc.subject | Volterra integral equation | |
| dc.subject | Weakly singular kernel | |
| dc.subject | Gronwall inequality | |
| dc.title | Initial value problems for Caputo fractional equations with singular nonlinearities | |
| dc.type | Article |