Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(3): 539-553

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.539

Copyright © The Korean Mathematical Society.

Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument

Mohamed Abdalla Darwish, Johnny Henderson, and Donal O'Regan

Damanhour University, Baylor University, National University of Ireland

Abstract

We study the solvability of a perturbed quadratic functional-integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.

Keywords: functional integral equation, fractional integral, perturbed, linear modification of the argument, existence, asymptotic behaviour, measure of noncompactness, Schauder fixed point principle

MSC numbers: 45G10, 45M99, 47H08