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

Authors:
Yong-Kui Chang;M. Mallika Arjunan;G. M. N'Guérékata;V. Kavitha
Affiliations:
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 7300070, PR China;Department of Mathematics, Karunya University, Karunya Nagar, Coimbatore-641 114, Tamil Nadu, India;Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA;Department of Mathematics, Karunya University, Karunya Nagar, Coimbatore-641 114, Tamil Nadu, India
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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