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J. Banas and A. Chlebowicz, “On Existence of Integrable Solutions of a Functional Integral Equation under Carathéodory Conditions,” Nonlinear Analysis, Vol. 70, No. 9, 2009, pp. 3172-3179.

has been cited by the following article:

• TITLE: Existence Theorem for a Nonlinear Functional Integral Equation and an Initial Value Problem of Fractional Order in L1(R+)

  AUTHORS: Ibrahim Abouelfarag Ibrahim, Tarek S. Amer, Yasser M. Aboessa

  KEYWORDS: Nonlinear Functional Integral Equation; Volterra Operator; Measure of Weak Noncompactness; Fractional Calculus; Schauder Fixed Point Theorem

  JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 28, 2013

  ABSTRACT: The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we deduce the existence of solution of an initial value problem of fractional order that be studied only on a bounded interval. The main tools used are Schauder fixed point theorem, measure of weak noncompactness, superposition operator and fractional calculus.