School of Basic Sciences
Indian Institute of Technology Mandi
Mandi, H.P. - 175001, India
email: sabbas.iitk@gmail.com, abbas@iitmandi.ac.in
Syed Abbas
Abstract:
In this article, we discuss the existence and uniqueness of
solution to fractional order ordinary and delay differential
equations. We apply our results on the single species model of
Lotka Volterra type. Fixed point theorems are the main tool used
here to establish the existence and uniqueness results. First we
use Banach contraction principle and then Krasnoselskii's fixed
point theorem to show the existence and uniqueness of the solution
under certain conditions. Moreover, we prove that the solution can
be extended to maximal interval of existence.
Submitted November 16, 2010. Published January 16, 2011.
Math Subject Classifications: 34K40, 34K14.
Key Words: Fractional differential equation;
fixed point theorems; maximum interval of existence.
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Syed Abbas School of Basic Sciences Indian Institute of Technology Mandi Mandi, H.P. - 175001, India email: sabbas.iitk@gmail.com, abbas@iitmandi.ac.in |
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