Weighted fractional differential equations with infinite delay in Banach spaces

Qixiang Dong, Can Liu, and Zhenbin Fan. "Weighted fractional differential equations with infinite delay in Banach spaces." Open Mathematics 14.1 (2016): 370-383. <http://eudml.org/doc/281187>.

@article{QixiangDong2016,
abstract = {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.},
author = {Qixiang Dong, Can Liu, Zhenbin Fan},
journal = {Open Mathematics},
keywords = {Fractional integral; Fractional derivative; Functional differential equation; Infinite delay; fractional derivative; functional differential equation; infinite delay},
language = {eng},
number = {1},
pages = {370-383},
title = {Weighted fractional differential equations with infinite delay in Banach spaces},
url = {http://eudml.org/doc/281187},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Qixiang Dong
AU - Can Liu
AU - Zhenbin Fan
TI - Weighted fractional differential equations with infinite delay in Banach spaces
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 370
EP - 383
AB - 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.
LA - eng
KW - Fractional integral; Fractional derivative; Functional differential equation; Infinite delay; fractional derivative; functional differential equation; infinite delay
UR - http://eudml.org/doc/281187
ER -