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2013 Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales
Ling Wu, Jiang Zhu
Abstr. Appl. Anal. 2013(SI05): 1-23 (2013). DOI: 10.1155/2013/795701


-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.


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Ling Wu. Jiang Zhu. "Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales." Abstr. Appl. Anal. 2013 (SI05) 1 - 23, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095365
MathSciNet: MR3143548
Digital Object Identifier: 10.1155/2013/795701

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI05 • 2013
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