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

Zhu Jiang | Zendy; Ying Zhu | Zendy

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Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales

Author(s) -

Zhu Jiang,

Ying Zhu

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 - 10.1155/2013/401596

Subject(s) - mathematics , derivative (finance) , scalable vector graphics , matrix (chemical analysis) , combinatorics , mathematical analysis , computer science , world wide web , materials science , composite material , financial economics , economics

The Δ-power function and fractional Δ-integrals and fractional Δ-differential are defined, and then thedefinitions and properties of Δ-Mittag-Leffler function are given. The properties of fractional Δ-integrals and fractional Δ-differential on time scales are discussed in detail. After that, theexistence of the solution and the dependency of the solution upon theinitial value for Cauchy type problem with fractional Δ-derivativeare studied. Also the explicit solutions to homogeneous fractional Δ-differential equations and nonhomogeneous fractional Δ-differentialequations are derived by using Laplace transform method

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