Weighted Stepanov-like pseudo-almost automorphic mild solutions for semilinear fractional differential equations

被引：3

作者：

He, Bing ^{[1
]}

Cao, Junfei ^{[1
]}

Yang, Bicheng ^{[1
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510310, Guangdong, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

weighted Stepanov-like pseudo-almost automorphic function; semilinear fractional differential equation; fractional relaxation-oscillation equation; solution operator; fractional integral; PERIODIC-SOLUTIONS; CAUCHY-PROBLEM; MASSERA TYPE; EXISTENCE; UNIQUENESS; THEOREM;

D O I：

10.1186/s13662-015-0410-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D(t)(alpha)x(t) = Ax(t) + D-t(alpha-1) F(t, x(t)), t is an element of R, where 1 < alpha < 2, A is a linear densely defined operator of sectorial type of omega < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.

引用

页码：1 / 36

页数：36

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