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Abstract and Applied Analysis
Volume 2015, Article ID 486054, 23 pages
http://dx.doi.org/10.1155/2015/486054
Research Article

Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales

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

Received 18 July 2014; Accepted 31 August 2014

Academic Editor: Dumitru Baleanu

Copyright © 2015 Jiang Zhu and Ling Wu. 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 definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo nabla derivative are studied. Also the explicit solutions to homogeneous equations and nonhomogeneous equations are derived by using Laplace transform method.