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Abstract and Applied Analysis
Volume 2014, Article ID 618434, 11 pages
Research Article

Existence and Characterization of Solutions of Nonlinear Volterra-Stieltjes Integral Equations in Two Variables

1Mathematics Department, Science Faculty for Girls, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Rzeszów University of Technology, Aleja Powstańców Warszawy 8, 35-959 Rzeszów, Poland

Received 7 February 2014; Accepted 29 April 2014; Published 18 May 2014

Academic Editor: Cemil Tunç

Copyright © 2014 Mohamed Abdalla Darwish and Józef Banaś. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper is devoted mainly to the study of the existence of solutions depending on two variables of a nonlinear integral equation of Volterra-Stieltjes type. The basic tool used in investigations is the technique of measures of noncompactness and Darbo’s fixed point theorem. The results obtained in the paper are applicable, in a particular case, to the nonlinear partial integral equations of fractional orders.