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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