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

被引：8
|
作者：
Zhu, Jiang [1 ]
Zhu, Ying [1 ]
机构：
[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
基金：
中国国家自然科学基金;
关键词：
D O I：
10.1155/2013/401596
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Delta-power function and fractional Delta-integrals and fractional Delta-differential are defined, and then the definitions and properties of Delta-Mittag-Leffler function are given. The properties of fractional Delta-integrals and fractional Delta-differential on time scales are discussed in detail. After that, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Delta-derivative are studied. Also the explicit solutions to homogeneous fractional Delta-differential equations and nonhomogeneous fractional Delta-differential equations are derived by using Laplace transform method.
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页数：19
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