Show simple item record

dc.contributor.authorWebb, Jeffrey ( Orcid Icon 0000-0001-7729-1123 )
dc.date.accessioned2021-12-06T16:00:24Z
dc.date.available2021-12-06T16:00:24Z
dc.date.issued2019-10-30
dc.identifier.citationWebb, J. R. L. (2019). Initial value problems for Caputo fractional equations with singular nonlinearities. Electronic Journal of Differential Equations, 2019(117), pp. 1-32.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15011
dc.description.abstractWe 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 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.formatText
dc.format.extent34 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional derivativesen_US
dc.subjectVolterra integral equationen_US
dc.subjectWeakly singular kernelen_US
dc.subjectGronwall inequalityen_US
dc.titleInitial value problems for Caputo fractional equations with singular nonlinearitiesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record