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Abstract and Applied Analysis
Volume 2013, Article ID 795701, 23 pages
http://dx.doi.org/10.1155/2013/795701
Research Article

Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Received 19 July 2013; Revised 22 September 2013; Accepted 22 September 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Ling Wu and Jiang Zhu. 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

-Laplace transform, fractional -power function, -Mittag-Leffler function, fractional -integrals, and fractional -differential on time scales are defined. Some of their properties are discussed in detail. After then, by using Laplace transform method, the existence of the solution and the dependency of the solution upon the initial value for Cauchy-type problem with the Riemann-Liouville fractional -derivative are studied. Also the explicit solutions to homogeneous equations and nonhomogeneous equations are derived by using Laplace transform method.