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

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

Mathematics Department, Faculty of Science and Education, Taif University, Al-Khurmah Branch, Taif, KSA.

DOI: 10.4236/am.2013.42060                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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