Translator Disclaimer
October 2019 Solutions to fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions
Jin Liang, Yunyi Mu, Ti-Jun Xiao
Banach J. Math. Anal. 13(4): 745-768 (October 2019). DOI: 10.1215/17358787-2019-0017

Abstract

We are concerned with fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions, where the operator pairs generate propagation families. With the help of the theory of propagation family and Laplace transforms, along with an estimate for a special sequence improved in this article, we introduce a definition of mild solutions to the impulsive problem for these abstract fractional Sobolev-type integro-differential equations and we establish general existence theorems and a continuous dependence theorem, which essentially extend some previous conclusions. In our results, the operator B could be unbounded, and the existence of an operator B1 is not necessarily needed. Moreover, we give some examples to illustrate our main results.

Citation

Download Citation

Jin Liang. Yunyi Mu. Ti-Jun Xiao. "Solutions to fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions." Banach J. Math. Anal. 13 (4) 745 - 768, October 2019. https://doi.org/10.1215/17358787-2019-0017

Information

Received: 24 December 2018; Accepted: 2 March 2019; Published: October 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07118761
MathSciNet: MR4016896
Digital Object Identifier: 10.1215/17358787-2019-0017

Subjects:
Primary: 34K37
Secondary: 46B50, 47A50, 47D06, 47D99, 47N20

Rights: Copyright © 2019 Tusi Mathematical Research Group

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.13 • No. 4 • October 2019
Back to Top