AM  Vol.4 No.2 , February 2013
Existence Theorem for a Nonlinear Functional Integral Equation and an Initial Value Problem of Fractional Order in L1(R+)
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.
Cite this paper: I. Ibrahim, T. Amer and Y. Aboessa, "Existence Theorem for a Nonlinear Functional Integral Equation and an Initial Value Problem of Fractional Order in L1(R+)," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 402-409. doi: 10.4236/am.2013.42060.

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