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.