On almost automorphic mild solutions for fractional semilinear initial value problems

被引：14

作者：

Chen, Anping ^{[1
,2
]}

Chen, Fulai ^{[1
]}

Deng, Siqing ^{[1
]}

机构：

[1] Xiangnan Univ, Dept Math, Chenzhou 423000, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411005, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 03期

关键词：

Fractional differential equation; Almost automorphic function; Mild solution; EXISTENCE;

D O I：

10.1016/j.camwa.2009.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates almost automorphic mild solutions of the fractional semilinear equation D(alpha)x(t) = Ax(t) + f(t, x(t)), 0 < alpha < 1, considered in a Banach space x, where A is a linear operator of sectorial type omega < 0. Some sufficient conditions are given for the existence, uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1318 / 1325

页数：8

共 50 条

[21] Pseudo almost automorphic solutions of fractional order neutral differential equation
Abbas, Syed
SEMIGROUP FORUM, 2010, 81 (03) : 393 - 404
[22] PSEUDO ALMOST AUTOMORPHIC SOLUTION OF SEMILINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES
Wang, Dingjiang
Xia, Zhinan
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2015, 18 (04) : 951 - 971
[23] Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
Sin, Chung-Sik
In, Hyok-Chol
Kim, Kwang-Chol
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[24] Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
Chung-Sik Sin
Hyok-Chol In
Kwang-Chol Kim
Advances in Difference Equations, 2018
[25] MILD SOLUTIONS FOR SEMILINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Mophou, Gisele M.
N'Guerekata, Gaston M.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2009,
[26] Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction-diffusion equations
Cao, Junfei
Huang, Zaitang
Zeng, Caibin
JOURNAL OF MATHEMATICAL CHEMISTRY, 2014, 52 (07) : 1984 - 2012
[27] The global existence of mild solutions for semilinear fractional Cauchy problems in the α-norm
Wang, Rong-Nian
Chen, De-Han
Wang, Yan
ANNALES POLONICI MATHEMATICI, 2012, 103 (02) : 161 - 173
[28] Pseudo almost automorphic solutions of fractional order neutral differential equation
Syed Abbas
Semigroup Forum, 2010, 81 : 393 - 404
[29] ALMOST AUTOMORPHIC SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS (vol 133, pg 2401, 2005)
Goldstein, J. A.
N'Guerekata, G. M.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (03) : 1111 - 1112
[30] Pseudo Almost Automorphic Solution of Semilinear Fractional Differential Equations with the Caputo Derivatives
Dingjiang Wang
Zhinan Xia
Fractional Calculus and Applied Analysis, 2015, 18 : 951 - 971

← 1 2 3 4 5 →