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2 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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On a mixed type integral equation and fractional-order functional differential equations

El-Sayed A. M. A., Sherif N., Ibrahim I. A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

237--247

In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval [0,1].

On an operator functional equation in L1 [0, ∞) and Volterra-Fredholm type integral equations

El-Sayed A. M. A., Sherif N., El-Farag I. A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(1)

61-76

The existence of a solution of a nonlinear operator functional equation in the class of monotonic functions on the interval R+ = [0, oo) is investigated. The approach to establish the main result is based on the notion of measure of noncompactness and an associated fixed point theorem due to Darbo. A Volterra-Fredholm type integral equation arises as a particular case of the investigated nonlinear operator functional equation.