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Volume 18,     Number 1,     Spring 2010

 

MONOTONIC SOLUTIONS OF NONLINEAR
INTEGRAL EQUATIONS OF FRACTIONAL
ORDER
ADEL JAWAHDOU AND ABDERRAZEK KAROUI

Abstract. In the first part of this paper, we use Schauder's fixed point theorem and prove an existence result of continuous and monotone solutions over bounded intervals of Urysohn's type nonlinear integral equation of fractional kind. In the second part of of this work, we extend the previous existence result to the case of a quadratic nonlinear integral equation of fractional order defined over R+, the half line of positive real numbers. The main ingredients used in the proof of the second existence result are the Tychonoff fixed point theorem associated with a measure of noncomapctness over C (R+). Some examples are provided to illustrate the different results of this work.

 

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