Monotonic solutions of a quadratic integral equation of fractional order

Abstract

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.

On Existence of Solutions of <i>q</i>-Perturbed Quadratic Integral Equations

“…Also, Banaś et al and Darwish [13] [15]- [17] studied quadratic integral equations of arbitrary orders with singular kernels. In [18], Darwish generalized and extended Banaś et al [15] results to the perturbed quadratic integral equations of arbitrary orders with singular kernels.…”

Existence of nondecreasing solutions of some nonlinear integral equations of fractional order

“…in [2]- [7] respectively. On the other hand M. Abdalla Darwish et al considered the following equations,…”

Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra

“…Many authors studied the existence of solutions for several classes of nonlinear quadratic integral equations (see e.g. [2]- [6] and [17]- [18]). However, in most of these papers, the main results are realized with the help of the technique associated with the measure of noncompactness.…”