Almost automorphic solutions to a class of semilinear fractional differential equations

被引：86

作者：

Cuevas, Claudio ^{[2
]}

Lizama, Carlos ^{[1
]}

机构：

[1] Univ Santiago Chile, Dept Matemat, Santiago, Chile

[2] Univ Fed Pernambuco, Dept Matemat, BR-50540740 Recife, PE, Brazil

来源：

APPLIED MATHEMATICS LETTERS | 2008年 / 21卷 / 12期

关键词：

Almost automorphic function; Solution operator; Fractional integral; Semilinear integro-differential equations;

D O I：

10.1016/j.aml.2008.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study almost automorphic (mild) solutions of the semilinear fractional equation delta(alpha)(t)u = Au + delta(alpha-1)(t)f (., u), 1 < alpha < 2, considered in a Banach space X, where A is a linear operator of sectorial type omega < 0. We prove the existence and uniqueness of an almost automorphic mild solution assuming that f (t, x) is almost automorphic in t for each x E X, satisfies some Lipschitz type conditions and takes values on X. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1315 / 1319

页数：5

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