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Mathematical Problems in Engineering
Volume 2015, Article ID 835891, 13 pages
http://dx.doi.org/10.1155/2015/835891
Research Article

Existence, Uniqueness, and Characterization Theorems for Nonlinear Fuzzy Integrodifferential Equations of Volterra Type

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
3Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University (KAU), Jeddah 21589, Saudi Arabia

Received 12 October 2014; Accepted 18 November 2014

Academic Editor: Jinhu Lü

Copyright © 2015 Omar Abu Arqub et al. 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.

Abstract

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed.