# Weighted fractional differential equations with infinite delay in Banach spaces

Qixiang Dong; Can Liu; Zhenbin Fan

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 370-383
- ISSN: 2391-5455

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topQixiang 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 -

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