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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 129478, 8 pages
http://dx.doi.org/10.1155/2013/129478
Research Article

Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Received 8 July 2013; Accepted 31 August 2013

Academic Editor: M. Victoria Otero-Espinar

Copyright © 2013 Dariusz Idczak 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

We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type. The proof of this result is based on a theorem on diffeomorphism between Banach and Hilbert spaces. The main assumption is the Palais-Smale condition.