This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.
@article{bwmeta1.element.doi-10_1515_math-2016-0035,
author = {Qixiang Dong and Can Liu and Zhenbin Fan},
title = {Weighted fractional differential equations with infinite delay in Banach spaces},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {370-383},
zbl = {1352.34104},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0035}
}
Qixiang Dong; Can Liu; Zhenbin Fan. Weighted fractional differential equations with infinite delay in Banach spaces. Open Mathematics, Tome 14 (2016) pp. 370-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0035/