Existence Theorem for a Nonlinear Functional Integral Equation and an Initial Value Problem of Fractional Order in L<sub>1</sub>(R<sub>+</sub>)

• 作者: Ibrahim Abouelfarag Ibrahim Tarek S. Amer Yasser M. Aboessa
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: NONLINEAR Functional Integral Equation VOLTERRA Operator Measure of Weak Noncompactness Fractional Calculus SCHAUDER Fixed Point Theorem
• 年，卷（期）: yysxyw,（2）
• 页码范围: 402-409
• 页数: 8页
• 分类号: O1

摘要

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.