Abstract
In this paper we study the existence of solution x ∈ L1 (0,1) for a functional integral equation. As an application we prove the existence of solution for an initial value problem of the fractional order. The main tools used are Schauder fixed point theorem, Lusin theorem and Scorza Dragoni theorem.
Highlights
The class of the integral equations, arises in several fields such as mathematical analysis, nonlinear functional analysis and mathematical physics [8],[9],[11],[15].In this work, we use Schauder fixed point theorem and a set of conditions on f1,f2, k1, k2 and g to prove the existence of L1−solution of equationReceived: November 6, 2013 §Correspondence author c 2014 Academic Publications, Ltd. url: www.acadpubl.euI
We use Schauder fixed point theorem and a set of conditions on f1,f2, k1, k2 and g to prove the existence of L1−solution of equation
The set of conditions we imposed to prove the existence of L1−solution of equation (1), turn to be naturally satisfied in some applications
Summary
The class of the integral equations, arises in several fields such as mathematical analysis, nonlinear functional analysis and mathematical physics [8],[9],[11],[15]. We use Schauder fixed point theorem and a set of conditions on f1,f2, k1, k2 and g to prove the existence of L1−solution of equation. The set of conditions we imposed to prove the existence of L1−solution of equation (1), turn to be naturally satisfied in some applications. We can apply our existence result to establish the existence of L1−solution of the initial value problem of fractional order dy(t) dt.
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