On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

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• 作者：Yong-Kui Chang^a ; ^{lzchangyk@163.com"" rel=""nofollow} ; M. Mallika Arjunan^b ; ^{arjunphd07@yahoo.co.in"" rel=""nofollow} ; G.M. N’ ; Gué ; ré ; kata^c ; ^{Gaston.N'Guerekata@morgan.edu"" rel=""nofollow} ; V. Kavitha^b ; ^{kavi_velubagyam@yahoo.co.in"" rel=""nofollow}
• 关键词：Fractional differential equations ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-52JDVDJ-2&_mathId=mml4&_pii=S089812211100191X&_issn=08981221&_acct=C000050441&_version=1&_userid=1019
• 刊名：Computers and Mathematics with Applications
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：62
• 期：3
• 页码：1228-1237
• 全文大小：258 K

文摘

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray–Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.