Geodesic
Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 71-86.

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We study the solvability of a perturbed quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. Finally, we give an example to illustrate our abstract results.
Keywords: Quadratic Integral Equation, Fractional Integral, Existence, Asymptotic Behaviour, Measure of Noncompactness, Darbo Fixed Point Theorem, 45G10, 45M99, 47H09 
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Darwish, Mohamed; Henderson, Johnny. Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 71-86. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a5/