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Abstract and Applied Analysis
Volume 2013, Article ID 401596, 19 pages
http://dx.doi.org/10.1155/2013/401596
Research Article

Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales

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

Received 9 August 2013; Accepted 6 October 2013

Academic Editor: Ali H. Bhrawy

Copyright © 2013 Jiang Zhu and Ying 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

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