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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