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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 806984, 4 pages
http://dx.doi.org/10.1155/2013/806984
Research Article

Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order

1School of Information Science & Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Avenida Padre Tomas Pereira, Taipa, Macau

Received 21 April 2013; Accepted 10 May 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Ming Li and Wei Zhao. 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

This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.