Fractional Cauchy problem with memory effects

Luciano Abadias and Edgardo Alvarez

Mathematische Nachrichten, 2020, vol. 293, issue 10, 1846-1872

Abstract: We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects CDtαu(t)−Au(t)+∫0tβ(t−s)Au(s)ds=f(t,u(t)),t∈[0,T],T>0,where u(0)=u0∈X and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study global or blow up mild solutions when the nonlinearity f satisfies a locally Lipschitz condition. The case of critical nonlinearities is also treated.

Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201800342

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:293:y:2020:i:10:p:1846-1872

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().