I. A. Ibrahim, T. S. Amer and Y. M. Abo Essa, “Integrable Solutions of Initial Value Problems of Fractional Order,” Far East Journal of Mathematical Sciences, Vol. 62, No. 1, 2012, pp. 97-123.

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.