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.
Highlights
The class of functional integral equations of various types plays very important role in numerous mathematical research areas
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+)
An interesting feature of functional integral equations is its role in the study of many problems of functional differential Equations [1,2,3,4]
Summary
The class of functional integral equations of various types plays very important role in numerous mathematical research areas. An interesting feature of functional integral equations is its role in the study of many problems of functional differential Equations [1,2,3,4]. In this work we study the solvability of the following initial value problem dy t dt. Where D y denotes the fractional derivative of order of y with 0,1. Such initial value problem of arbitrary order (1) was investigated in [5,6,7]. To achieve this goal, let us consider the integral equation x t f.
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