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

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

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 resu...

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Published in:Electronic journal of differential equations Vol. 2011; no. 9; pp. 1 - 11
Main Author: Syed Abbas
Format: Journal Article
Language:English
Published: Texas State University 2011
Subjects:
fixed point theorems
Fractional differential equation
maximum interval of existence
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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.
AbstractList 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.
Author Syed Abbas
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Snippet 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...
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SubjectTerms fixed point theorems
Fractional differential equation
maximum interval of existence
Title Existence of solutions to fractional order ordinary and delay differential equations and applications
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