Cauchy problem for a class of fractional differential equations on time scales

Abstract

In this work, the concept of fractional calculus on time scales is developed to the study of fractional differential equations on time scales. By using the Banach contraction principle and the Schauder fixed-point theorem, some existence results for fractional differential equations on time scales are obtained. Finally, an example is given to illustrate the main results.

Keywords:

• time scales
• fractional calculus
• fractional differential equations
• Cauchy problem

2010 AMS Subject Classifications:

• 34A08
• 34N05
• 34A12

Acknowledgements

The authors thank the anonymous referee for his/her careful reading of this manuscript and many helpful suggestions. This work has been supported by the National Natural Science Foundation of China (11071108) and the Provincial Natural Science Foundation of Jiangxi, China (2010GZS0147,20114BAB201007).