Electron. J. Diff. Equ., Vol. 2011 (2011), No. 09, pp. 1-11.

Existence of solutions to fractional order ordinary and delay differential equations and applications

Syed Abbas

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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