Abstract and Applied Analysis

Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales

Ling Wu and Jiang Zhu

Full-text: Open access

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 795701, 23 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450376

Digital Object Identifier
doi:10.1155/2013/795701

Mathematical Reviews number (MathSciNet)
MR3143548

Zentralblatt MATH identifier
07095365

Citation

Wu, Ling; Zhu, Jiang. Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 795701, 23 pages. doi:10.1155/2013/795701. https://projecteuclid.org/euclid.aaa/1393450376


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