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 On Urysohn-Volterra fractional quadratic integral equations Keywords:Fractional integral, quadratic integral equation, monotonic solutions, Darbo theorem, monotonicity measure of noncompactness. Abstract: In this paper the authors study a fractional quadratic integral equation of Urysohn-Volterra type. They show that the integral equation has at least one monotonic solution in the Banach space of all real functions defined and continuous on the interval $[0,1]$. The main tools in the proof are a fixed point theorem due to Darbo and a monotonicity measure of noncompactness.