μ-pseudo almost automorph mild solutions to the fractional integro-differential equation with uniform continuity

被引:0
|
作者
Gu, Chuan-Yun [1 ,2 ]
Li, Hong-Xu [1 ]
机构
[1] Sichuan Univ, Dept Math, Chengdu, Sichuan, Peoples R China
[2] Sichuan Univ Arts & Sci, Dept Math, Dazhou, Peoples R China
来源
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
关键词
Mild solutions; mu-S-p-pseudo almost automorphy; Fixed point theorem; Fractional integro-differential equation; STEPANOV-LIKE PSEUDO; WEIGHTED PSEUDO;
D O I
10.1186/s13662-018-1518-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Our aim in the article is to study the existence of mu-pseudo almost automorph mild solutions to the following fractional integro-differential equation: D(alpha)u(t) = Au(t) + integral(t)(-infinity) a(t - s)Au(s) ds + f (t, u(t)), t is an element of R, where for alpha > 0, the fractional derivative D-alpha is understood in the sense of Weyl, and A is a closed linear operator defined on Banach space X, a is an element of L-loc(1)(R+) is a scalar-valued kernel. The novelty of this work is a study of this equation with a mu-S-p-pseudo almost automorph nonlinear term satisfying the condition of "uniform continuity" instead of some "Lipschitz" type conditions supposed in the literature. We utilize Schauder's fixed point theorem. An example is provided to explain our abstract results.
引用
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页数:13
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