Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales | Zendy

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Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales

Author(s) -

Ling Wu,

Zhu Jiang

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/795701

Subject(s) - mathematics , derivative (finance) , scalable vector graphics , matrix (chemical analysis) , combinatorics , computer science , chemistry , chromatography , financial economics , economics , operating system

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. © 2013 Ling Wu and Jiang Zhu.

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